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Constitutive sets of convex static systems. (English) Zbl 1146.70009

Summary: We formulate the principle of virtual work for dissipative systems. Partially controlled systems are discussed, and the concept of a generating families of forms is introduced. The notion of a critical point of a family of convex forms is introduced and discussed. A number of examples are given.

MSC:

70G75 Variational methods for problems in mechanics
70Q05 Control of mechanical systems
49S05 Variational principles of physics
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References:

[1] Marmo, G.; Tulczyjew, W.; Urbański, R., Dynamics of autonomous systems with external forces, Acta Phys. Polon., B 33, 1181-1240 (2002) · Zbl 1066.70011
[2] Rockafellar, R., (Convex Analysis (1970), Princeton University Press: Princeton University Press Princeton) · Zbl 0193.18401
[3] Tulczyjew, W. M., The origin of variational principles, (Grabowski, J.; Marrno, G.; Urbafiski, R., Classical and Quantum lntegrability (2003), Banach Center Publications 59: Banach Center Publications 59 Warsaw), 41-75 · Zbl 1074.70010
[4] Tulczyjew, W. M.; Urbański, E., A slow and careful Legendre transformation for singular Lagrangians, Acta Phys. Polon., B 30, 2909-2978 (1999) · Zbl 1010.70015
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