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Publication 23-CNA-009

Action principles for dissipative, non-holonomic Newtonian mechanics

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213

Ambar N. Sengupta
Department of Mathematics
University of Connecticut
Storrs, CT 06269

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.

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