Symplectic and Cosymplectic Reduction for Simple Hybrid Forced Mechanical Systems with Symmetries

Colombo, Leonardo; León, Manuel de; Irazú, María Emma Eyrea; Asier, López-Gordón,

doi:10.2139/ssrn.4089151

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…Furthermore, we plan to study hybrid contact Hamiltonian and Lagrangian systems. Hybrid systems are an alternative formalism for describing physical system with impacts, as well as certain unmanned aerial vehicles systems and legged robots (for instance, see [5] and references therein).…”

Section: Discussionmentioning

confidence: 99%

Contact Lagrangian systems subject to impulsive constraints

Colombo¹,

León²,

Asier³

2022

J. Phys. A: Math. Theor.

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We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily plane and a rolling sphere on a non-uniform plane, both with dissipation.

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Section: Discussionmentioning

confidence: 99%

Contact Lagrangian systems subject to impulsive constraints

Colombo¹,

León²,

Asier³

2022

J. Phys. A: Math. Theor.

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Geometric Hamilton–Jacobi theory for systems with external forces

León

Valcázar

Asier

2022

Journal of Mathematical Physics

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In this paper, we develop a Hamilton–Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems, and present some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton–Jacobi problem for forced Hamiltonian systems with symmetry. Furthermore, we consider the reduction of the Hamilton–Jacobi problem for a Čaplygin system to the Hamilton–Jacobi problem for a forced Lagrangian system.

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Orientation Control of the Bouncing Ball

Clark

Kassabova

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Symplectic and Cosymplectic Reduction for Simple Hybrid Forced Mechanical Systems with Symmetries

Cited by 3 publications

References 20 publications

Contact Lagrangian systems subject to impulsive constraints

Contact Lagrangian systems subject to impulsive constraints

Geometric Hamilton–Jacobi theory for systems with external forces

Orientation Control of the Bouncing Ball

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