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We start with Lagrange's equations of motion for the generalized coordinates, written in generalized force form.
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Classroom Contents
Lagrange’s Equations with Conservative and Non-Conservative Forces - Phase Space Introduction
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- 1 We start with Lagrange's equations of motion for the generalized coordinates, written in generalized force form.
- 2 We decompose the applied forces into conservative (those coming from a potential energy U) and non-conservative forces. Those which come from a potential energy U can be absorbed into a Lagrangian f…
- 3 We then work on a couple of examples using this method.
- 4 We then write Lagrange's equations for a system of rigid bodies, where now the kinetic energy includes translational and rotational kinetic energy, and the projection vectors are of two types, one f…
- 5 Some worked examples of some rigid body systems.
- 6 We introduce the idea of phase space and phase portraits, a method for finding and classifying the possible motions (i.e., solving the equations of motion) and analyzing the characteristics of the m…
