The Dynamics of Constrained Motion
Firdaus E. Udwadia
University of Southern California
Department of Aerospace and Mechanical Engineering
Los Angeles, California
Wed, Sept. 21, 2022 - 4:00 PM
This talk deals with the development of the general explicit equations of motion for nonlinear mechanical systems subjected to holonomic and nonholonomic equality constraints. The use of Gauss’s principle yields the explicit equation of motion without the notion of Lagrange multipliers being invoked. The resulting equations show the simplicity, efficacy, and aesthetic with which Nature orchestrates constrained motion. Working like a control engineer using feedback control, she ensures that the constraints are exactly satisfied at each instant of time. Extensions to systems (1) with singular mass matrices (2) systems in which the number of coordinates exceeds the minimum number and (3) systems in which d’Alemebert’s prescription may need to be extended, are shown. The ramifications of the results on the obverse problem of the control of nonlinear mechanical systems is also broached.
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