Academic literature on the topic 'Hamiltonien non convexe'
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Journal articles on the topic "Hamiltonien non convexe"
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Ishii, Hitoshi. "The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence." Mathematics in Engineering 5, no. 4 (2023): 1–10. http://dx.doi.org/10.3934/mine.2023072.
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<abstract><p>In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian in the gradient variable, for which the full convergence of the solutions does not hold as the discount factor tends to zero. We give here an explicit example of nonlinear monotone systems of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the full convergence of the solutions fails as the discount factor goes to zero.</p></abstract>
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Timoumi, Mohsen. "Solutions périodiques de systèmes hamiltoniens convexes non coercitifs." Bulletin de la Classe des sciences 75, no. 1 (1989): 463–81. http://dx.doi.org/10.3406/barb.1989.57866.
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Cirant, Marco, and Alessio Porretta. "Long time behavior and turnpike solutions in mildly non-monotone mean field games." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 86. http://dx.doi.org/10.1051/cocv/2021077.
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We consider mean field game systems in time-horizon (0, T), where the individual cost functional depends locally on the density distribution of the agents, and the Hamiltonian is locally uniformly convex. We show that, even if the coupling cost functions are mildly non-monotone, then the system is still well posed due to the effect of individual noise. The rate of anti-monotonicity (i.e. the aggregation rate of the cost functions) which can be afforded depends on the intensity of the diffusion and on global bounds of solutions. We give applications to either the case of globally Lipschitz Hamiltonians or the case of quadratic Hamiltonians and couplings having mild growth. Under similar conditions, we investigate the long time behavior of solutions and we give a complete description of the ergodic and long term properties of the system. In particular we prove: (i) the turnpike property of solutions in the finite (long) horizon (0, T), (ii) the convergence of the system from (0, T) towards (0, ∞), (iii) the vanishing discount limit of the infinite horizon problem and the long time convergence towards the ergodic stationary solution. This way we extend previous results which were known only for the case of monotone and smoothing couplings; our approach is self-contained and does not need the use of the linearized system or of the master equation.
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CONTRERAS, GONZALO, and RENATO ITURRIAGA. "Convex Hamiltonians without conjugate points." Ergodic Theory and Dynamical Systems 19, no. 4 (August 1999): 901–52. http://dx.doi.org/10.1017/s014338579913387x.
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We construct the Green bundles for an energy level without conjugate points of a convex Hamiltonian. In this case we give a formula for the metric entropy of the Liouville measure and prove that the exponential map is a local diffeomorphism. We prove that the Hamiltonian flow is Anosov if and only if the Green bundles are transversal. Using the Clebsch transformation of the index form we prove that if the unique minimizing measure of a generic Lagrangian is supported on a periodic orbit, then it is a hyperbolic periodic orbit.We also show some examples of differences with the behaviour of a geodesic flow without conjugate points, namely: (non-contact) flows and periodic orbits without invariant transversal bundles, segments without conjugate points but with crossing solutions and non-surjective exponential maps.
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Hayat, Sakander, Muhammad Yasir Hayat Malik, Ali Ahmad, Suliman Khan, Faisal Yousafzai, and Roslan Hasni. "On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes." Mathematical Problems in Engineering 2021 (July 17, 2021): 1–18. http://dx.doi.org/10.1155/2021/5553216.
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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.
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Pittman, S. M., E. Tannenbaum, and E. J. Heller. "Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian." Journal of Chemical Physics 145, no. 5 (August 7, 2016): 054303. http://dx.doi.org/10.1063/1.4960134.
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Monthus, Cécile. "Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and via explicit large deviations at various levels." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 6 (June 1, 2023): 063206. http://dx.doi.org/10.1088/1742-5468/acdcea.
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Abstract For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker–Planck dynamics involving an arbitrary force F(x) and an arbitrary diffusion coefficient D(x), or in discrete space with the Markov jump dynamics involving arbitrary nearest-neighbor transition rates w ( x ± 1 , x ) , the Markov generator can be transformed via an appropriate similarity transformation into a quantum supersymmetric Hamiltonian with many remarkable properties. We first describe how the mapping from the boundary-driven non-equilibrium dynamics towards some dual equilibrium dynamics (see Tailleur et al 2008 J. Phys. A: Math. Theor. 41 505001) can be reinterpreted via the two corresponding quantum Hamiltonians that are supersymmetric partners of each other, with the same energy spectra. We describe the consequences for the spectral decomposition of the boundary-driven dynamics, and we give explicit expressions for the Kemeny times needed to converge towards the non-equilibrium steady states. We then focus on the large deviations at various levels for empirical time-averaged observables over a large time-window T. We start with the always explicit Level 2.5 concerning the joint distribution of the empirical density and of the empirical flows before considering the contractions towards lower levels. In particular, the rate function for the empirical current alone can be explicitly computed via the contraction from the Level 2.5 using the properties of the associated quantum supersymmetric Hamiltonians.
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Hayat, Sakander, Asad Khan, Suliman Khan, and Jia-Bao Liu. "Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index." Complexity 2021 (January 23, 2021): 1–23. http://dx.doi.org/10.1155/2021/6684784.
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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.
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Zhou, Min, and Binggui Zhong. "Regions of applicability of Aubry-Mather Theory for non-convex Hamiltonian." Chinese Annals of Mathematics, Series B 32, no. 4 (July 2011): 605–14. http://dx.doi.org/10.1007/s11401-011-0654-3.
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Entov, Michael, and Leonid Polterovich. "Contact topology and non-equilibrium thermodynamics." Nonlinearity 36, no. 6 (May 17, 2023): 3349–75. http://dx.doi.org/10.1088/1361-6544/acd1ce.
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Abstract We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.
Dissertations / Theses on the topic "Hamiltonien non convexe"
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Aslani, Shahriar. "Bumpy metric theorem in the sense of Mañé for non-convex Hamiltonian vector fields." Electronic Thesis or Diss., Université Paris sciences et lettres, 2022. http://www.theses.fr/2022UPSLE038.
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Une propriété est générique au sensé de Mañé si, donné un Hamiltonien H : T∗M → ℝ, l’ensemble des fonctions lisses u : M → ℝ tel que H + u vérifie la propriété est un sous-ensemble générique de C∞(M). Notre objectif est de savoir dans quelle mesure la non dégénérescence de toutes les orbites périodiques dans un niveau d’énergie donné d’un Hamiltonien lisse non convexe est une propriété générique au sensé de Mañé. Où la nondégénérescence signifie que dérivée de l’application de Poincaré ne prend pas les racines de l’unité comme une valeurs propre. Pour atteindre cet objectif, nous obtiendrons un théorème de perturbation pour les aplication de Poincaré similaire au théorème de Rifford et Ruggiero dans le cadre convexe, et une forme normale de type Fermi sur les orbites d’un champ de vecteurs Hamiltonien non convexe. Ce sont deux outils applicables à l’étude de la dynamique des champs de vecteurs Hamiltoniens non convexes. D’autre part, nous montrerons que dans les cas convexes et non convexes, nous avons certainement besoin d’un mécanisme différent pour prouver le théorème des métrique bosselées pour les orbites symétriques. Une orbite symétrique est une orbite dont la projection sur les variétés de base comprend soit des points d’auto-intersection, soit des points à vitesse nulle. Ce fait a été négligé dans les études précédentes. Une étude détaillée des formes normales locales sur les segments d’orbite d’un champ de vecteurs Hamiltonien est donnée. Cela inclut une forme normale pour les Hamiltoniens convexes, une forme normale pour les Hamiltoniens positivement homogènes qui implique la forme normale de Li-Nienberg pour les métriques de Finsler, et comme nous l’avons mentionné une forme normale pour les Hamiltoniens non convexes. De cette façon, nous éliminons la confusion qui existe dans la littérature entre la forme normale de Li-Nirenberg et une forme normale souhaitée similaire pour les champs de vecteurs Hamiltoniens convexesA property (p) of smooth Hamiltonian vector fields is called Mañé-generic whenever the set of smooth potentials u such that H + u satisfies the property (p) is a generic subset. Given a non-convex smooth Hamiltonian H : T∗M → ℝ which is defined on the cotangent bundle of a smooth manifold M, our goal in this thesis is to know that to what extend non-degeneracy of all periodic orbits in a given energy level of H is a Mañé generic property. Where by a periodic non-degenerate orbit we mean a periodic orbit that its associated linearized Poincaré map does not take roots of unity as an eigenvalue. To that end, we will achieve a perturbation theorem for linearized Poincaré maps similar to Rifford and Ruggiero’s theorem in the convex setting, and a Fermi-like normal form on orbits of a non-convex Hamiltonian vector field. These are two applicable tools in the study of non-convex Hamiltonian vector fields. At the other hand, we will show that in both convex and non-convex cases we certainly need a different machinery to prove the bumpy metric theorem for symmetric orbits. A symmetric orbit is an orbit that its projection on the base manifolds includes either self-intersection points or points with zero velocity. This fact was overlooked in previous studies. A detailed study of local normal forms on orbit segments of a Hamiltonian vector field is given. That includes a normal form for convex Hamiltonians, a normal form for positively homogeneous Hamiltonians that implies Li-Nienberg normal form for Finsler metrics, and as we mentioned a normal form for non-convex Hamiltonians. In this way, we remove the confusion that exists in the literature between Li-Nirenberg normal form and a similar desired normal form for convex Hamiltonian vector fields
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Ranty, François. "Systèmes hamiltoniens convexes présentant une intégrale première non triviale." Paris 9, 1987. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1987PA090018.
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Une solution d'un système hamiltonien autonome reste sur des surfaces de niveau constant pour chaque fonction en involution avec l'hamiltonien. Ces fonctions sont les intégrales premières du système. On considère deux surfaces de niveau de deux hamiltoniens f et g en involution, et on cherche un système hamiltonien particulier tel que l'une de ses solutions périodiques soit entièrement tracée sur l'intersection des deux surfaces. Moyennant des hypothèses sur les solutions périodiques d'index zéro ou un tracé sur l'une ou l'autre des surfaces, on démontre l'existence d'un troisième hamiltonien k, en involution avec f et g, et d'une solution périodique du système hamiltonien associe à k tracée toute entière sur l'intersection des deux niveaux d'énergie initiaux
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Ranty, François. "Systèmes hamiltoniens convexes présentant une intégrale première non triviale." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37609184p.
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Roos, Valentine. "Solutions variationnelles et solutions de viscosité de l'équation de Hamilton-Jacobi." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLED023/document.
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On étudie l'équation de Hamilton-Jacobi évolutive du premier ordre, couplée avec une donnée initiale lipschitzienne. Le but est de comparer les solutions de viscosité et les solutions variationnelles pour cette équation, deux notions de solutions faibles qui coïncident en dynamique hamiltonienne convexe. Pour travailler dans un cadre pertinent pour les deux types de solutions, on doit d’abord construire une solution variationnelle sans hypothèse de compacité sur la variété ou le hamiltonien étudiés. On retrace dans ce cas la construction historique des solutions variationnelles, en détaillant les propriétés de la famille génératrice obtenue par la méthode des géodésiques brisées. Il en découle des estimées permettant d’obtenir la solution de viscosité à partir de la solution variationnelle par un procédé d’itération. Après avoir vérifié que la solution variationnelle construite coïncide effectivement avec la solution de viscosité pour un Hamiltonien convexe, on caractérise les Hamiltoniens intégrables pour lesquels cette propriété persiste, en étudiant attentivement des exemples élémentaires en dimension 1 et 2We study the first order Hamilton-Jacobi equation associated with a Lipschitz initial condition. The purpose of this thesis is to compare two notions of weak solutions for this equation, namely the viscosity solution and the variational solution, that are known to coincide in convex Hamiltonian dynamics. In order to work in a relevant framework for both notions, we first need to build a variational solution without compactness assumption on the manifold or the Hamiltonian. To do so, we follow the historical construction, detailing properties of the generating family obtained via the broken geodesics method. Local estimates allow to prove that the viscosity solution can be obtained from the variational solution via an iterative process. We then check that this construction gives effectively the viscosity solution for a convex Hamiltonian, and characterize the integrable Hamiltonians for which this property persists by carefully studying elementary examples in dimension 1 and 2
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Imbert, Cyril. "Analyse non lisse : fonction d'appui de la jacobienne généralisée de Clarke : quelques applications aux équations de Hamilton-Jacobi du premier ordre (formules de Hopf-Lax, hamiltoniens diff. Convexes, enveloppes de solutions sci)." Phd thesis, Toulouse 3, 2000. http://www.theses.fr/2000TOU30036.
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Le travail presente dans ce memoire est divise en deux parties distinctes. La premiere partie est consacree aux calculs des fonctions d'appui de la jacobienne generalisee de clarke et de son enveloppe pleniere, associees a une fonction localement lipschtizienne a valeurs vectorielles. Clarke avait etabli en 1975 que la fonction d'appui du sous-differentiel generalise etait une derivee directionnelle generalisee. Il est donc satisfaisant de constater que la fonction d'appui de la jacobienne generalisee est une sorte divergence generalisee. Dans la seconde partie, nous presentons un certain nombre d'applications de techniques issues de l'analyse non lisse a la resolution d'equations de hamilton-jacobi du premier ordre. Ainsi nous utilisons la dualite convexe et le calcul sous-differentiel pour prouver que les formules dites de hopf-lax definissent des solutions explicites des equations de hamilton-jacobi associees (avec donnees initiales semicontinues inferieurement). Nous n'utilisons ni le fameux principe de comparaison de la theorie des solutions de viscosite ni regularisation. Nous traitons successivement le cas de la dimension finie et de la dimension infinie. Ces resultats nous permettent de trouver des estimations des solutions d'equations dont l'hamiltonien est la difference de deux fonctions convexes. Enfin, nous nous attachons a l'etude des solutions sci dans des espaces de banach dits lisses. Le theoreme de la valeur moyenne de clarke et ledyaev nous permet de montrer un resultat d'enveloppe : nous construisons une solution sci pour une equation dont l'hamiltonien est le supremum d'une famille d'hamiltoniens. Nous appliquons enfin les memes techniques pour prouver l'existence d'une solution sci minimale sous des hypotheses plus faibles que celles que l'on rencontre generalement dans la litterature. .
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Imbert, Cyril. "Analyse non lisse : - Fonction d'appui de la Jacobienne généralisée de Clarke et de son enveloppe plénière - Quelques applications aux équations de Hamilton-Jacobi du premier ordre (fonctions de Hopf-Lax, Hamiltoniens diff. convexes, solutions sci)." Phd thesis, Université Paul Sabatier - Toulouse III, 2000. http://tel.archives-ouvertes.fr/tel-00001203.
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Le travail présenté dans ce mémoire est divisé en deux parties. La première partie est consacrée aux calculs des fonctions d'appui de la Jacobienne généralisée de Clarke et de son enveloppe plénière, associées à une fonction localement lipschtizienne à valeurs vectorielles. Clarke avait établi en 1975 que la fonction d'appui du sous-différentiel généralisé était une dérivée directionnelle généralisée. Il est donc satisfaisant de constater que la fonction d'appui de la Jacobienne généralisée est une sorte de "divergence directionnelle généralisée". Dans la seconde partie, nous présentons un certain nombre d'applications de techniques issues de l'Analyse non lisse à la résolution d'équations de Hamilton-Jacobi du premier ordre. Ainsi nous utilisons la dualité convexe et le calcul sous-différentiel pour prouver que les formules dites de Hopf-Lax définissent des solutions explicites des équations de Hamilton-Jacobi associées (avec données initiales semicontinues inférieurement). Nous n'utilisons ni le fameux principe de comparaison de la théorie des solutions de viscosité ni régularisation. Nous traitons successivement le cas de la dimension finie et de la dimension infinie. Ces résultats nous permettent de trouver des estimations des solutions d'équations dont l'hamiltonien est la différence de deux fonctions convexes. Enfin, nous nous attachons à l'étude des solutions sci dans des espaces de Banach dits ``lisses''. Le théorème de la valeur moyenne de Clarke et Ledyaev nous permet de montrer un résultat d'``enveloppe'' : nous construisons une solution sci pour une équation dont l'hamiltonien est le supremum d'une famille d'hamiltoniens. Nous appliquons enfin les mêmes techniques pour prouver l'existence d'une solution sci minimale sous des hypothèses plus faibles que celles que l'on recontre généralement dans la littérature.
Books on the topic "Hamiltonien non convexe"
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Mann, Peter. Partial Differentiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0032.
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This short chapter discusses the Legendre transform, which is used in mechanics to convert between the Lagrangian and the Hamiltonian formulations. The Legendre transform is a mathematical tool that can be used to convert the variables of a function through the methods of partial differentiation in a one-to-one fashion. Developed by Adrien-Marie Legendre in the nineteenth century, it is also central to converting between action principles, generating functions and thermodynamic potentials. By using the Legendre transform, two variables can be expressed in four different ways, via the idea of conjugate pairs; it just depends on what differential quantity is subtracted. Variables that are not considered in the transformation are called passive variables, whiles the important ones are the active variables. The information in this chapter provides the background for many of the other chapters in this book.
Book chapters on the topic "Hamiltonien non convexe"
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Salmon, Rick. "Hamiltonian Fluid Dynamics." In Lectures on Geophysical Fluid Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195108088.003.0010.
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In this final chapter, we return to the subject of the first: the fundamental principles of fluid mechanics. In chapter 1, we derived the equations of fluid motion from Hamilton’s principle of stationary action, emphasizing its logical simplicity and the resulting close correspondence between mechanics and thermodynamics. Now we explore the Hamiltonian approach more fully, discovering its other advantages. The most important of these advantages arise from the correspondence between the symmetry properties of the Lagrangian and the conservation laws of the resulting dynamical equations. Therefore, we begin with a very brief introduction to symmetry and conservation laws. Noether’s theorem applies to the equations that arise from variational principles like Hamilton’s principle. According to Noether’s theorem : If a variational principle is invariant to a continuous transformation of its dependent and independent variables, then the equations arising from the variational principle possess a divergence-form conservation law. The invariance property is also called a symmetry property. Thus Noether’s theorem connects symmetry properties and conservation laws. We shall neither state nor prove the general form of Noether’s theorem; to do so would require a lengthy digression on continuous groups. Instead we illustrate the connection between symmetry and conservation laws with a series of increasingly complex and important examples. These examples convey the flavor of the general theory. Our first example is very simple. Consider a body of mass m moving in one dimension. The body is attached to the end of a spring with spring-constant K. Let x(t) be the displacement of the body from its location when the spring is unstretched.
Conference papers on the topic "Hamiltonien non convexe"
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Spada, Fabio, Pietro Ghignoni, Afonso Botelho, Gabriele De Zaiacomo, and Paulo Rosa. "Successive convexification-based fuel-optimal high-altitude guidance of the RETALT reusable launcher." In ESA 12th International Conference on Guidance Navigation and Control and 9th International Conference on Astrodynamics Tools and Techniques. ESA, 2023. http://dx.doi.org/10.5270/esa-gnc-icatt-2023-161.
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The last decade witnessed the major boost in space services since the beginning of space commercial activities. Development of reusable launchers has played a fundamental role in such advancement: cuts in refurbishment costs have indeed positively impacted on the financial needs to access stable operational orbits. In this context, the EU and ESA have made increasing efforts to achieve the goal of making launcher reusability the state of the art in Europe. One such effort is RETALT (Retro Propulsion-Assisted Landing Technologies) a Horizon 2020 project that allowed to increase the TRL of key technologies that will enable retro propulsion-assisted launcher reusability in Europe (Marwege, et al., 2022). In particular, one of the enabling technologies for launchers’ recovery through vertical landing is indeed GNC. Reliable and performing GNC algorithms are necessary to perform terminal manoeuvres autonomously and precisely within a limited available time horizon. In RETALT, a GNC solution was developed and brought to TRL3, assessing its performance considering uncertainties and dispersions on the vehicle and environmental models (Ghignoni, et al., 2022). On the other hand, dispersions at stage separation, i.e. the beginning of the re-entry arc, heavily impact on booster trajectory, and, if not properly managed, prevent the rocket from being able to reach the landing site. Leveraging on the work done in RETALT, Deimos continued improving the GNC solution for reusable launchers, aiming at increasing the knowledge of the problem and the robustness of the algorithms. This paper focuses on the high-altitude guidance solution for the downrange landing (DRL) of the first stage of RETALT1, a two-stage-to-orbit (TSTO) launcher studied within RETALT. The DRL mission foresees an initial ballistic arc and two distinct burns connected by an aerodynamic phase. A high-altitude firing (re-entry burn) aims at reducing aerothermal loads, while the terminal landing burn guarantees a soft pinpoint landing on a floating barge. The first aim of the work is combining state-of-the-art indirect and direct techniques to design a re-entry burn guidance capable of handling stage separation dispersions, while guaranteeing compliance with mass, online guidance and attitude requirements. Indirect methods are used in an offline fashion: the free-final time Hamiltonian boundary value problem stemming from the first-order optimality necessary conditions of the fuel-optimal 3DoF optimal entry guidance problem is solved at first. This is done for a finite number of sample points drawn from the dispersed initial conditions and a grid of ignition heights. A lookup table mapping initial conditions to optimal ignition height is thus obtained and used to schedule the beginning of the firing. Convex direct methods are used onboard, and a continuation technique is adopted to obtain a guidance profile compatible with attitude constraints: the 3DoF dynamics problem is solved first; its solution is then fed to a second iteration embedding nonlinear attitude kinematics and satisfying attitude rate limitations. The second aim of the work is validating the guidance algorithm in a high-fidelity simulation environment. The DEIMOS-proprietary RETALT Functional Engineering Simulator (RETALT-FES) is used for such purpose; it includes detailed vehicle configurations and mission scenario models contributing to simulate a real-life scenario with GNC algorithms in the loop. In the full-length paper the algorithm will be then proved capable of handling such further dispersions. The full proposed strategy, therefore, presents itself as a mid-ground with respect to uncertainties handling: the most relevant ones, i.e. the ones associated with separation conditions, are included within the guidance scheme, while the remaining ones are contained with the standard feedback-based control strategies. Bibliography Ghignoni, P. et al., 2022. RETALT: Recovery GNC for the Retro-Propulsive Vertical Landing of an Orbital Launch Vehicle. Bruges, HiSST2022. Marwege, A. et al., 2022. RETALT: review of technologies and overview of design changes. CEAS Space Journal.