Academic literature on the topic 'Einstein constraint system'

The notion of the formless found a lasting definition in Documents, the dissident Surrealist magazine led by Georges Bataille, Carl Einstein and Michel Leiris from 1929 to 1931. In an unassuming short entry for its ‘Dictionnaire’, Bataille presents the informe emphatically not as a system or a structure, but as ‘un terme servant à déclasser’; yet neither the disruptive impulse of the 'Dictionnaire', nor the more recent exhibitions it has generated, can avoid a measure of taxonomic organisation (L'Informe: mode d'emploi, 1996; Undercover Surrealism, 2006). In the realm of poetry, free verse has eroded the boundaries of the poetic, but its freedom from formal constraints is limited too; as Jay Parini (2008) contends, ‘formless poetry does not really exist, as poets inevitably create patterns in language that replicate forms of experience.’ Through a small number of case studies, this chapter will consider the legacy of Bataille’s definition while assessing the ongoing tension between form and its undoing in textual and visual art of the twenty-first century.

Statistical mechanics is clearly mechanics (classical, quantum, special or general relativistic, or any other) plus the theory of probabilities, as is well known. It is our understanding, however, that it is more than that. It is also the adoption of a specific entropic functional, which will, in some sense, adequately shortcut the vast, and for most practical purposes useless, detailed microscopic mechanical information on the system. It is, in particular, through this functional that the connection with thermodynamics and its macroscopic laws will be established. This particular functional is determined by the specific type (or geometry) of occupation of the phase space (or Hilbert space or analogous space). This geometrical structure depends in turn not only on the microscopic dynamics that the system obeys, but also on the initial conditions at which the system is placed at t = 0. In colloquial terms, we could say that the microscopic dynamics determine where the system is allowed to live, whereas the initial conditions determin where it likes to live within the allowed region. This viewpoint is consistent with Einstein's perspective on classical statistical mechanics, and especially with his criticism [82, 92] of the celebrated Boltzmann principle However, the problem is that, up to now, no systematic manner exists for univocally determining the entropic functional to be used, given the dynamics and the initial conditions. The optimization of this entropy under the physically appropriate constraints is expected to provide the correct probability distribution for the microscopic states of the macroscopic stationary state of the system. Boltzmann, then complemented by Gibbs, proposed the celebrated form which is the foundation of standard statistical mechanics.

This paper presents an algorithm for modeling the dynamics of multi-rigid body systems in generalized topologies including topologies with closed kinematic loops that may or may not be coupled together. The algorithm uses a hierarchic assembly disassembly process in parallel implementation and a recursive assembly disassembly process in serial implementation to achieve highly efficient simulation turn-around times. The kinematic constraints are imposed using the formalism of kinematic joints that are modeled using motion spaces and their orthogonal complements. A mixed set of coordinates are u