Formulation of the Governing Equations of Motion of Dynamic Systems on a Principal Bundle

DOI10.5890/JAND.2020.03.011zbMath1441.70008OpenAlexW3000500085MaRDI QIDQ5121763

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Publication date: 19 September 2020

Published in: Journal of Applied Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5890/jand.2020.03.011

zbMATH Keywords

dynamical systemsequations of motiondifferential geometrygeometric mechanicsprincipal bundles

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Applications of global differential geometry to the sciences (53C80) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Nonholonomic systems related to the dynamics of a system of particles (70F25)

Cites Work

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• Sensitivity analysis for multibody systems formulated on a Lie group
• The d'Alembert-Lagrange equation exploited on a Riemannian manifold
• Another form of equations of motion for constrained multibody systems
• A Lie group formulation of Kane's equations for multibody systems
• On the equivalence of Kane's equations and Gibbs' equations for multibody dynamics formulations
• Equations of motion of a multibody system and Lie groups
• Constraint forces and undetermined multipliers in constrained multibody systems
• On the governing equations of motion of nonholonomic systems on Riemannian manifolds
• Kane’s Equations With Undetermined Multipliers—Application to Constrained Multibody Systems
• The Boltzmann-Hamel equations for the optimal control of mechanical systems with nonholonomic constraints
• Motivating Kane's method for obtaining equations of motion for dynamic systems
• Dynamics of Nonholonomic Systems
• Formulation of Equations of Motion for Complex Spacecraft
• Multibody structural dynamics including translation between the bodies
• A geometrical interpretation of Kane’s Equations
• An Energy Theorem for Developing Testing Functions for Numerical Simulations of Dynamic Systems
• Another Look at Nonholonomic Systems
• Testing the accuracy of numerical simulations of multibody systems