Complete dynamical PDE systems of one-dimensional nonlinear elasticity satisfying the principle of material frame indifference are derived in Eulerian and Lagrangian formulations. These systems are considered within the framework of equivalent nonlocally related PDE systems. Consequently, a direct relation between the Euler and Lagrange systems is obtained. Moreover, other equivalent PDE system...

Abstract The homogeneous causal action principle on a compact domain of momentum space is introduced. connection to fermion systems worked out. Existence and compactness results are reviewed. Euler–Lagrange equations derived analyzed under suitable regularity assumptions.

Preface During the 1996-97 academic year, Phillip Griffiths and Robert Bryant conducted a seminar at the Institute for Advanced Study in Princeton, NJ, outlining their recent work (with Lucas Hsu) on a geometric approach to the calculus of variations in several variables. The present work is an outgrowth of that project; it includes all of the material presented in the seminar, with numerous ad...

In this position paper, we seek to extend the layered perception-action paradigm for on-line learning such that it includes an explicit symbolic processing capability. By incorporating symbolic processing at the apex of the perception action hierarchy in this way, we ensure that abstract symbol manipulation is fully grounded, without the necessity of specifying an explicit representational fram...

We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is supported on the intersection of a hyperplane with a level set of a function which is homogeneous of degree two. Moreover, we perform second variations to obtain t...

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noetherlike theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define...

The statistical bundle is the set of couples (Q, W) of a probability density Q and a random 1 variable W such that EQ [W] = 0. On a finite state space, we assume Q to be a probability density with 2 respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is 3 a model for Information Geometry. Velocity and accelleration of a one-dimensional statisti...

Abstract. It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manifold. Then properties of other dynamical systems can be studied rela...

A Lagrangian-Hamiltonian variational formulation is proposed for the thermoelasticity of heat conductors and its generalization to anelasticity described by means of internal-state variablesby using a gauge-theoretical technique (introduction of an additional variable of state the gradient of thermacy that renders the system apparently Hamiltonian). Projecting the equations resulting from the E...