English

Action principles for dissipative, non-holonomic Newtonian mechanics

Mathematical Physics 2024-07-02 v4 Dynamical Systems math.MP Classical Physics

Abstract

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and positions, is presented. Methods for incorporating constraints are critically assessed. General theory, as well as explicitly worked out variational principles for a dissipative system (due to Lorenz) and a system with anholonomic constraints (due to Pars) are demonstrated. Conditions under which a (family of) dual Hamiltonian flow(s), as well as a constant(s) of motion, may be associated with a conservative or dissipative, and possibly constrained, primal system naturally emerge in this work.

Keywords

Cite

@article{arxiv.2306.10616,
  title  = {Action principles for dissipative, non-holonomic Newtonian mechanics},
  author = {Amit Acharya and Ambar N. Sengupta},
  journal= {arXiv preprint arXiv:2306.10616},
  year   = {2024}
}

Comments

to be published in Proceedings of the Royal Society A