Lagrange’s Equations, Hamilton’s Equations, and Kane’s Equations: Interrelations, Energy Integrals, and a Variational Principle

[+] Author and Article Information
D. L. Mingori

Mechanical, Aerospace, and Nuclear Engineering Department, 38-137 Engineering IV, University of California, Los Angeles, CA 90024-1597

J. Appl. Mech 62(2), 505-510 (Jun 01, 1995) (6 pages) doi:10.1115/1.2895958 History: Received March 15, 1993; Revised October 15, 1993; Online October 30, 2007


A new viewpoint is suggested for expressing the governing equations of analytical mechanics. This viewpoint establishes a convenient framework for examining the relationships among Lagrange’s equations, Hamilton’s equations, and Kane’s equations. The conditions which must be satisfied for the existence of an energy integral in the context of Kane’s equations are clarified, and a generalized form of Hamilton’s Principle is presented. Generalized speeds replace generalized velocities as the velocity variables in the formulation. The development considers holonomic systems in which the generalized forces are derivable from a potential function.

Copyright © 1995 by The American Society of Mechanical Engineers
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