Mathematical Methods of Classical Mechanics

TL;DR: In this article, the connection between the Kolmogorov-Sinai entropy rate and the time evolution of the physical or statistical entropy S is elucidated for a large family of chaotic conservative dynamical systems including the simplest ones.

TL;DR: An analogy between nonequilibrium dynamics and mappings between equilibrium ensembles is described, which suggests that the practical inferiority of fast switching is quite general and the relevance of adiabatic invariants in slowly driven Hamiltonian systems for the application of Jarzynski's theorem is discussed.

TL;DR: Lectures on Analytical Mechanics is a comprehensive textbook covering the fundamentals of analytical mechanics and its applications in various fields of physics. It provides a detailed overview of the subject, including key concepts like Lagrangian and Hamiltonian formalisms, normal oscillations, and canonical transformations.

TL;DR: In this paper, a numerical timeintegration scheme for the dynamics of nonlinear elastic shells is presented that simultaneously and independent of the time-step size inherits exactly the conservation laws of total linear, total angular momentum as well as total energy.