Unified formalism for higher-order variational problems and its applications in optimal control
2014 ◽
Vol 11
(04)
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pp. 1450034
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In this paper, we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner–Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics. As an interesting application we deduce the equations of motion for optimal control of underactuated mechanical systems defined on principal bundles.
2014 ◽
Vol 6
(4)
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pp. 451-478
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1991 ◽
Vol 55
(4)
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pp. 555-559
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2020 ◽
Vol 26
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pp. 37
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Keyword(s):
2021 ◽
Vol 502
(3)
◽
pp. 3976-3992
Keyword(s):
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