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Articoli di riviste sul tema "Matrix mechanics"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 29 luglio 2024

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1

Little, J. Paige, Clayton Adam, Graeme Pettet e Mark J. Pearcy. "Initiation of Mechanical Derangement in the Anulus Fibrosus Ground Matrix(Soft Tissue Mechanics)". Proceedings of the Asian Pacific Conference on Biomechanics : emerging science and technology in biomechanics 2004.1 (2004): 183–84. http://dx.doi.org/10.1299/jsmeapbio.2004.1.183.

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2

Kawamura, Y. "Generalized Matrix Mechanics". Progress of Theoretical Physics 107, n. 6 (1 giugno 2002): 1105–15. http://dx.doi.org/10.1143/ptp.107.1105.

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3

Anninos, Dionysios, Frederik Denef e Ruben Monten. "Grassmann matrix quantum mechanics". Journal of High Energy Physics 2016, n. 4 (aprile 2016): 1–26. http://dx.doi.org/10.1007/jhep04(2016)138.

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4

Tschang, Y. "Matrix Mechanics and Hadron Statics". Physics Essays 10, n. 2 (giugno 1997): 315–26. http://dx.doi.org/10.4006/1.3028718.

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5

Betzios, P., U. Gürsoy e O. Papadoulaki. "Matrix quantum mechanics onS1/Z2". Nuclear Physics B 928 (marzo 2018): 356–414. http://dx.doi.org/10.1016/j.nuclphysb.2018.01.019.

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6

Bebiano, N., J. da Providência e R. Lemos. "Matrix inequalities in statistical mechanics". Linear Algebra and its Applications 376 (gennaio 2004): 265–73. http://dx.doi.org/10.1016/j.laa.2003.07.004.

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7

Kawamura, Y. "Structure of Cubic Matrix Mechanics". Progress of Theoretical Physics 109, n. 1 (1 gennaio 2003): 1–10. http://dx.doi.org/10.1143/ptp.109.1.

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8

Perovic, Slobodan. "Why were Matrix Mechanics and Wave Mechanics considered equivalent?" Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39, n. 2 (maggio 2008): 444–61. http://dx.doi.org/10.1016/j.shpsb.2008.01.004.

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9

SHALYT-MARGOLIN, A. E., e J. G. SUAREZ. "QUANTUM MECHANICS AT PLANCK'S SCALE AND DENSITY MATRIX". International Journal of Modern Physics D 12, n. 07 (agosto 2003): 1265–78. http://dx.doi.org/10.1142/s0218271803003700.

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In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies in the fact that here the density matrix are subjected to deformation, whereas in the previous approaches only commutators are deformed. The density matrix obtained by deforming the quantum-mechanical one is named the density pro-matrix throughout this paper. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows a description of the dynamics. In particular, the explicit form of the deformed Liouville's equation and the deformed Shrödinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that the results obtained here allow one to deduce in a simple and natural way the Bekenstein–Hawking's formula for black hole entropy in semiclassical approximation.

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10

Marshall, D. B., B. N. Cox e A. G. Evans. "The mechanics of matrix cracking in brittle-matrix fiber composites". Acta Metallurgica 33, n. 11 (novembre 1985): 2013–21. http://dx.doi.org/10.1016/0001-6160(85)90124-5.

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11

Wagenseil, Jessica E., e Robert P. Mecham. "Vascular Extracellular Matrix and Arterial Mechanics". Physiological Reviews 89, n. 3 (luglio 2009): 957–89. http://dx.doi.org/10.1152/physrev.00041.2008.

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An important factor in the transition from an open to a closed circulatory system was a change in vessel wall structure and composition that enabled the large arteries to store and release energy during the cardiac cycle. The component of the arterial wall in vertebrates that accounts for these properties is the elastic fiber network organized by medial smooth muscle. Beginning with the onset of pulsatile blood flow in the developing aorta, smooth muscle cells in the vessel wall produce a complex extracellular matrix (ECM) that will ultimately define the mechanical properties that are critical for proper function of the adult vascular system. This review discusses the structural ECM proteins in the vertebrate aortic wall and will explore how the choice of ECM components has changed through evolution as the cardiovascular system became more advanced and pulse pressure increased. By correlating vessel mechanics with physiological blood pressure across animal species and in mice with altered vessel compliance, we show that cardiac and vascular development are physiologically coupled, and we provide evidence for a universal elastic modulus that controls the parameters of ECM deposition in vessel wall development. We also discuss mechanical models that can be used to design better tissue-engineered vessels and to test the efficacy of clinical treatments.

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12

Muntz, Iain, Michele Fenu, Gerjo J. V. M. van Osch e Gijsje H. Koenderink. "The role of cell–matrix interactions in connective tissue mechanics". Physical Biology 19, n. 2 (18 gennaio 2022): 021001. http://dx.doi.org/10.1088/1478-3975/ac42b8.

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Abstract Living tissue is able to withstand large stresses in everyday life, yet it also actively adapts to dynamic loads. This remarkable mechanical behaviour emerges from the interplay between living cells and their non-living extracellular environment. Here we review recent insights into the biophysical mechanisms involved in the reciprocal interplay between cells and the extracellular matrix and how this interplay determines tissue mechanics, with a focus on connective tissues. We first describe the roles of the main macromolecular components of the extracellular matrix in regards to tissue mechanics. We then proceed to highlight the main routes via which cells sense and respond to their biochemical and mechanical extracellular environment. Next we introduce the three main routes via which cells can modify their extracellular environment: exertion of contractile forces, secretion and deposition of matrix components, and matrix degradation. Finally we discuss how recent insights in the mechanobiology of cell–matrix interactions are furthering our understanding of the pathophysiology of connective tissue diseases and cancer, and facilitating the design of novel strategies for tissue engineering.

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13

Copeland, E. "Quantum Mechanics in Simple Matrix Form". Physics Bulletin 37, n. 11 (novembre 1986): 465. http://dx.doi.org/10.1088/0031-9112/37/11/035.

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14

Masters, Barry R. "Werner Heisenberg’s Path to Matrix Mechanics". Optics and Photonics News 25, n. 7 (10 luglio 2014): 42. http://dx.doi.org/10.1364/opn.25.7.000042.

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15

Jordan, Thomas F., e Kannan Jagannathan. "Quantum Mechanics in Simple Matrix Form". American Journal of Physics 54, n. 12 (dicembre 1986): 1154–55. http://dx.doi.org/10.1119/1.14691.

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16

Dietz, B., e F. Haake. "Random Matrix Theory as Statistical Mechanics". Europhysics Letters (EPL) 9, n. 1 (1 maggio 1989): 1–6. http://dx.doi.org/10.1209/0295-5075/9/1/001.

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17

Yukalov, V. I. "Matrix order indices in statistical mechanics". Physica A: Statistical Mechanics and its Applications 310, n. 3-4 (luglio 2002): 413–34. http://dx.doi.org/10.1016/s0378-4371(02)00783-5.

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18

Dai, Jian, e Yong-Shi Wu. "Quiver mechanics for deconstructed matrix string". Physics Letters B 576, n. 1-2 (dicembre 2003): 209–18. http://dx.doi.org/10.1016/j.physletb.2003.09.083.

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19

Angerer, Wolfgang P., e Adolfo Zamora. "Eigenvalues of a statistical mechanics matrix". Journal of Mathematical Chemistry 50, n. 6 (29 febbraio 2012): 1411–19. http://dx.doi.org/10.1007/s10910-012-9980-2.

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20

Kawamura, Y. "Cubic Matrix, Nambu Mechanics and Beyond". Progress of Theoretical Physics 109, n. 2 (1 febbraio 2003): 153–68. http://dx.doi.org/10.1143/ptp.109.153.

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21

Yang, Chun, Frank W. DelRio, Hao Ma, Anouk R. Killaars, Lena P. Basta, Kyle A. Kyburz e Kristi S. Anseth. "Spatially patterned matrix elasticity directs stem cell fate". Proceedings of the National Academy of Sciences 113, n. 31 (19 luglio 2016): E4439—E4445. http://dx.doi.org/10.1073/pnas.1609731113.

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There is a growing appreciation for the functional role of matrix mechanics in regulating stem cell self-renewal and differentiation processes. However, it is largely unknown how subcellular, spatial mechanical variations in the local extracellular environment mediate intracellular signal transduction and direct cell fate. Here, the effect of spatial distribution, magnitude, and organization of subcellular matrix mechanical properties on human mesenchymal stem cell (hMSCs) function was investigated. Exploiting a photodegradation reaction, a hydrogel cell culture substrate was fabricated with regions of spatially varied and distinct mechanical properties, which were subsequently mapped and quantified by atomic force microscopy (AFM). The variations in the underlying matrix mechanics were found to regulate cellular adhesion and transcriptional events. Highly spread, elongated morphologies and higher Yes-associated protein (YAP) activation were observed in hMSCs seeded on hydrogels with higher concentrations of stiff regions in a dose-dependent manner. However, when the spatial organization of the mechanically stiff regions was altered from a regular to randomized pattern, lower levels of YAP activation with smaller and more rounded cell morphologies were induced in hMSCs. We infer from these results that irregular, disorganized variations in matrix mechanics, compared with regular patterns, appear to disrupt actin organization, and lead to different cell fates; this was verified by observations of lower alkaline phosphatase (ALP) activity and higher expression of CD105, a stem cell marker, in hMSCs in random versus regular patterns of mechanical properties. Collectively, this material platform has allowed innovative experiments to elucidate a novel spatial mechanical dosing mechanism that correlates to both the magnitude and organization of spatial stiffness.

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22

Chen, Hui, Folian Yu, Bing Wang, Chenmin Zhao, Xiayu Chen, Walter Nsengiyumva e Shuncong Zhong. "Elastic Fibre Prestressing Mechanics within a Polymeric Matrix Composite". Polymers 15, n. 2 (13 gennaio 2023): 431. http://dx.doi.org/10.3390/polym15020431.

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The elastic fibre prestressing (EFP) technique has been developed to balance the thermal residual stress generated during curing of a polymeric composite. The continuous fibre reinforcements are prestressed and then impregnated into a polymeric matrix, where the prestress load is only removed after the resin is fully cured in order to produce an elastically prestressed polymeric matrix composite (EPPMC). Although the EFP is active in improving the static mechanical performance of a composite, its mechanics on dynamic mechanical performance and viscoelasticity of a composite is still limited. Here, we established a theoretical model in order to decouple the EFP principle, aiming to better analyse the underlying mechanics. A bespoke fibre prestressing rig was then developed to apply tension on a unidirectional carbon-fibre-reinforced epoxy prepreg to produce EPPMC samples with various EFP levels. The effects of EFP were then investigated by carrying out both static and dynamic mechanical testing, as well as the viscoelastic creep performance. It was found that there is an optimal level of EFP in order to maximise the prestress benefits, whilst the EFP is detrimental to the fibre/matrix interface. The EFP mechanisms are then proposed based on these observations to reveal the in-plane stress evolutions within a polymeric composite.

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23

Han, Yu Long, Pierre Ronceray, Guoqiang Xu, Andrea Malandrino, Roger D. Kamm, Martin Lenz, Chase P. Broedersz e Ming Guo. "Cell contraction induces long-ranged stress stiffening in the extracellular matrix". Proceedings of the National Academy of Sciences 115, n. 16 (4 aprile 2018): 4075–80. http://dx.doi.org/10.1073/pnas.1722619115.

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Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing nonlinear stress inference microscopy (NSIM), a technique to infer stress fields in a 3D matrix from nonlinear microrheology measurements with optical tweezers. Using NSIM and simulations, we reveal large long-ranged cell-generated stresses capable of buckling filaments in the matrix. These stresses give rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which can provide a mechanism for mechanical communication between cells.

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24

Lee, Stacey, e Sanjay Kumar. "Actomyosin stress fiber mechanosensing in 2D and 3D". F1000Research 5 (7 settembre 2016): 2261. http://dx.doi.org/10.12688/f1000research.8800.1.

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Mechanotransduction is the process through which cells survey the mechanical properties of their environment, convert these mechanical inputs into biochemical signals, and modulate their phenotype in response. These mechanical inputs, which may be encoded in the form of extracellular matrix stiffness, dimensionality, and adhesion, all strongly influence cell morphology, migration, and fate decisions. One mechanism through which cells on planar or pseudo-planar matrices exert tensile forces and interrogate microenvironmental mechanics is through stress fibers, which are bundles composed of actin filaments and, in most cases, non-muscle myosin II filaments. Stress fibers form a continuous structural network that is mechanically coupled to the extracellular matrix through focal adhesions. Furthermore, myosin-driven contractility plays a central role in the ability of stress fibers to sense matrix mechanics and generate tension. Here, we review the distinct roles that non-muscle myosin II plays in driving mechanosensing and focus specifically on motility. In a closely related discussion, we also describe stress fiber classification schemes and the differing roles of various myosin isoforms in each category. Finally, we briefly highlight recent studies exploring mechanosensing in three-dimensional environments, in which matrix content, structure, and mechanics are often tightly interrelated. Stress fibers and the myosin motors therein represent an intriguing and functionally important biological system in which mechanics, biochemistry, and architecture all converge.

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25

Rothschilds, R. J., L. B. Ilcewicz, P. Nordin e S. H. Applegate. "The Effect of Hygrothermal Histories on Matrix Cracking in Fiber Reinforced Laminates". Journal of Engineering Materials and Technology 110, n. 2 (1 aprile 1988): 158–68. http://dx.doi.org/10.1115/1.3226025.

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Environmental factors that affect matrix cracking in composite laminates include temperature, moisture content, and hygrothermal history. Matrix cracking in laminates exposed to aircraft environments was modelled using a fracture mechanics approach based on strain energy release rates. Residual stress relaxation due to hygrothermal history was found to alter the static mechanical strain necessary to cause matrix cracking in experiments. Depending on material type and hygrothermal history, this effect was shown to either increase or decrease the resistance to matrix cracking. Close agreement between predicted and measured strains at the onset of matrix cracking was obtained using a modification to the fracture mechanics approach. Viscoelastic stress relaxation was modelled as shifts in the stress free temperature. This approach seems feasible providing that matrix crack growth is an elastic phenomena. Matrix crack growth in laminates subjected to creep loads and severe environments may require the development of viscoelastic failure criteria.

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26

Sherlock, B. E., J. Chen, J. C. Mansfield, E. Green e C. P. Winlove. "Biophotonic tools for probing extracellular matrix mechanics". Matrix Biology Plus 12 (dicembre 2021): 100093. http://dx.doi.org/10.1016/j.mbplus.2021.100093.

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27

Sun, Bo. "The mechanics of fibrillar collagen extracellular matrix". Cell Reports Physical Science 2, n. 8 (agosto 2021): 100515. http://dx.doi.org/10.1016/j.xcrp.2021.100515.

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28

Majji, Manoranjan. "Regular Celestial Mechanics and the Matrix Exponential". Journal of Guidance, Control, and Dynamics 43, n. 11 (novembre 2020): 2127–32. http://dx.doi.org/10.2514/1.g005237.

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29

More, Richard M. "Semiclassical matrix-mechanics. II. Angular momentum operators". Journal de Physique II 1, n. 2 (febbraio 1991): 97–121. http://dx.doi.org/10.1051/jp2:1991150.

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30

Bender, Carl M., L. M. Simmons e Richard Stong. "Matrix methods in discrete-time quantum mechanics". Physical Review D 33, n. 8 (15 aprile 1986): 2362–66. http://dx.doi.org/10.1103/physrevd.33.2362.

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31

More, R. M. "Semiclassical matrix mechanics. I. The harmonic oscillator". Journal de Physique 51, n. 1 (1990): 47–58. http://dx.doi.org/10.1051/jphys:0199000510104700.

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32

Conlon, J. G. "A matrix diagonalisation problem in quantum mechanics". Journal of Physics A: Mathematical and General 20, n. 18 (21 dicembre 1987): 6281–91. http://dx.doi.org/10.1088/0305-4470/20/18/028.

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33

Savvidy, George K. "Loop transfer matrix and loop quantum mechanics". Journal of High Energy Physics 2000, n. 09 (27 settembre 2000): 044. http://dx.doi.org/10.1088/1126-6708/2000/09/044.

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34

Berg, J., e A. Engel. "Matrix Games, Mixed Strategies, and Statistical Mechanics". Physical Review Letters 81, n. 22 (30 novembre 1998): 4999–5002. http://dx.doi.org/10.1103/physrevlett.81.4999.

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35

Chiang, Y. C. "Mechanics of Matrix Cracking in Bonded Composites". Journal of Mechanics 23, n. 2 (giugno 2007): 95–106. http://dx.doi.org/10.1017/s172771910000112x.

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AbstractIn this paper, a general matrix cracking model including the effect of fiber/matrix debonding in the crack wake is developed for a unidirectional fiber reinforced composite. The debonding mechanics is incorporated into matrix cracking model by treating the crack-wake debonding as a particular crack propagation problem along the interface. Then, the closed-form analytical solution of the critical stress for the onset of widespread matrix cracking is derived, based on the analysis of steady state crack growth in the matrix. The fracture mechanics approach adopted in the present analysis is compared with the analysis in which the crack-wake debonding mechanics was modeled by energy balance approach. The conditions for attaining no-debonding and debonding as onset of widespread matrix cracking are discussed in terms of the interfacial properties of debond toughness and frictional shear stress. The theoretical results are compared with experimental data that are available in the literature.

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36

Suki, Béla, e Jason H. T. Bates. "Extracellular matrix mechanics in lung parenchymal diseases". Respiratory Physiology & Neurobiology 163, n. 1-3 (novembre 2008): 33–43. http://dx.doi.org/10.1016/j.resp.2008.03.015.

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37

Anglès d'Auriac, J. Ch, e J. M. Maillard. "Random matrix theory in lattice statistical mechanics". Physica A: Statistical Mechanics and its Applications 321, n. 1-2 (aprile 2003): 325–33. http://dx.doi.org/10.1016/s0378-4371(02)01756-9.

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38

HALPERN, M. B., e C. SCHWARTZ. "THE ALGEBRAS OF LARGE N MATRIX MECHANICS". International Journal of Modern Physics A 14, n. 19 (30 luglio 1999): 3059–119. http://dx.doi.org/10.1142/s0217751x99001482.

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Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: the Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

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39

Djemai, A. E. F. "Quantum mechanics as a matrix symplectic geometry". International Journal of Theoretical Physics 36, n. 2 (febbraio 1997): 571. http://dx.doi.org/10.1007/bf02435751.

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40

Pandey, Mahul, e Sachindeo Vaidya. "Yang–Mills matrix mechanics and quantum phases". International Journal of Geometric Methods in Modern Physics 14, n. 08 (11 maggio 2017): 1740009. http://dx.doi.org/10.1142/s0219887817400096.

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The [Formula: see text] Yang–Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The [Formula: see text] Yang–Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

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Sergi, Alessandro. "Matrix Algebras in Non-Hermitian Quantum Mechanics". Communications in Theoretical Physics 56, n. 1 (luglio 2011): 96–98. http://dx.doi.org/10.1088/0253-6102/56/1/18.

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Djemai, A. E. F. "Quantum mechanics as a matrix symplectic geometry". International Journal of Theoretical Physics 35, n. 3 (marzo 1996): 519–56. http://dx.doi.org/10.1007/bf02082821.

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Djemai, A. E. F. "Quantum mechanics as a matrix symplectic geometry". International Journal of Theoretical Physics 35, n. 3 (marzo 1996): 556. http://dx.doi.org/10.1007/bf02082822.

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Farmany, Abbas, Roshanak Lotfikar, Shahryar Abbasi, Ali Naghipour e Amin Farmany. "Non-commutative geometry and matrix quantum mechanics". Chaos, Solitons & Fractals 42, n. 1 (ottobre 2009): 62–64. http://dx.doi.org/10.1016/j.chaos.2008.10.021.

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Huang, Sui, e Donald E. Ingber. "Cell tension, matrix mechanics, and cancer development". Cancer Cell 8, n. 3 (settembre 2005): 175–76. http://dx.doi.org/10.1016/j.ccr.2005.08.009.

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46

Ferretti, G. "Chiral symmetry breaking in matrix quantum mechanics". Physics Letters B 284, n. 3-4 (giugno 1992): 325–30. http://dx.doi.org/10.1016/0370-2693(92)90439-b.

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47

Lakshmibala, S. "Heisenberg, matrix mechanics, and the uncertainty principle". Resonance 9, n. 8 (agosto 2004): 46–56. http://dx.doi.org/10.1007/bf02837577.

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48

Wang, Dafu, Travis Brady, Lakshmi Santhanam e Sharon Gerecht. "The extracellular matrix mechanics in the vasculature". Nature Cardiovascular Research 2, n. 8 (10 agosto 2023): 718–32. http://dx.doi.org/10.1038/s44161-023-00311-0.

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49

Bеlovol, Oleksandr. "Benefits of using matrix methods in teach-ing mechanics in higher education institu-tions". Bulletin of Kharkov National Automobile and Highway University 1, n. 101 (30 giugno 2023): 183. http://dx.doi.org/10.30977/bul.2219-5548.2023.101.0.183.

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Abstract (sommario):

Problem. Basic concepts, concepts, principles of mechanics are mainly taught from simple to complex in institutions of higher technical education, which to some extent resembles a course on the history of mechanics. In today's conditions, the education system is required to take into account current trends in scientific and engineering fields. The use of inherently geometric methods of vector algebra and vector analysis as a basis for studying mechanics is losing its relevance. To a certain extent, this approach interferes with the use of multidimensional spaces (configurational and phase), tensor algebra, and computer technologies in modeling complex mechanical systems. Goal. The goal is to expand the field of application of the matrix formalism to infinite-dimensional spaces, justify its advantages compared to other approaches used in teaching the basics of mechanical disciplines, and demonstrate its capabilities in solving complex practical problems, both in terms of modeling and in terms of using computer technologies. Methodology. The methodological basis for choosing matrix methods is the use of infinite-dimensional and abstract, in physical terms, spaces when studying the movement of mechanical systems. The fundamental impossibility of accurately describing the state of a mechanical system requires the use of statistical modeling methods and the extension of the so-called law of conservation of matter in the form of a balance equation to these models. Results. It is shown that the matrix method, which is widely used in quantum mechanics and very limited in classical mechanics, allows you to use the advantages of the transition to phase space when obtaining canonical equations and when solving problems of kinematics and dynamics of a solid body. Originality. The paper proposes certain improvements of the matrix apparatus, related to the use of geometric parameters of the mechanical system as indexes. That is, infinite-dimensional matrices with real coefficients are used. Practical value. The proposed method allows you to effectively solve the problems of the mechanics of an absolutely rigid body without using any theorems of the general course, remaining within the limits of standard mathematical training.

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黄, 永义. "The Dirac-Jordan Transformation Theory—From Matrix Mechanics to Wave Mechanics". Modern Physics 11, n. 02 (2021): 15–20. http://dx.doi.org/10.12677/mp.2021.112003.

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