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Dynamics of variable systems and Lie groups. (Russian, English) Zbl 1122.70332
Prikl. Mat. Mekh. 68, No. 6, 899-905 (2004); translation in J. Appl. Math. Mech. 68, No. 6, 803-808 (2004).
The paper deals with mechanical systems whose configuration space is a Lie group and whose Lagrangian is invariant with respect to the left shifts on this group. It is assumed that system masses geometry can be changed under the action of only internal forces. Conditions are discussed under which due to the masses geometry change the system can be transferred from the initial state to any prescribed one.

70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
76B99 Incompressible inviscid fluids
Full Text: DOI
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