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On the poincaré and chetayev equations

✍ Scribed by V.V Rumyantsev

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
417 KB
Volume
62
Category
Article
ISSN
0021-8928

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✦ Synopsis

The Lie group of virtual displacement operators in Rodrigues-Hamilton parameters is constructed and equations of motion are derived for a heavy rigid body with one fixed point. It is shown that the addition (subtraction) of a term of the form dr~dr, f(t, x) ~ C 2, to (from) the generalized Lagrangian L*(t, x, ~) does not affect the form of the Poincar~ and Chetayev equations.

These equations can also be used to describe the relative motion of a holonomic system relative to a moving system of coordinates. Hamel's equations in non-linear quasi-coordinates are derived without using the transitivity equations, are compared with the generalized Poincar6 equations and are transformed to Chetayev canonical form.

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