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Gauge theory of the falling cat. (English) Zbl 0787.70020
Enos, Michael J. (ed.), Dynamics and control of mechanical systems. The falling cat and related problems. Papers of the first Fields Institute Workshop held at Waterloo, Ontario (Canada), March 1992. Providence, RI: American Mathematical Society. Fields Inst. Commun. 1, 193-218 (1993).
Deformable bodies in free fall with zero angular momentum are represented by $$SO(3)$$ groups. The shape space and the configuration space are well suited for gauge groups. The main result is: The differential equations which must be solved to calculate the reorientation induced by any control strategy can be reduced to a single quadrature.
For the entire collection see [Zbl 0777.00030].

##### MSC:
 70Q05 Control of mechanical systems 70E99 Dynamics of a rigid body and of multibody systems 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 74M05 Control, switches and devices (“smart materials”) in solid mechanics