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Dynamics of variable systems and lie groups

✍ Scribed by V.V. Kozlov

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 459 KB
Volume: 68
Category: Article
ISSN: 0021-8928
DOI: 10.1016/j.jappmathmech.2004.11.001

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✦ Synopsis

Mechanical systems whose configuration space is a Lie group and whose Lagrangian is invariant to left translations on that group are considered. It is assumed that the mass geometry of the system may change under the action of only internal forces. The equations of motion admit of a complete set of Noether integrals which are linear in the velocities. For fixed values of these integrals, the equations of motion reduce to a non-autonomous system of first-order differential equations on the Lie group. Conditions under which the system can be brought from any initial position to another preassigned position by changing its mass geometry are discussed. The "falling cat" problem and the problem of the motion of a body of variable shape in an unlimited volume of ideal fluid are considered as examples.

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