Mechanical systems naturally evolve on principal bundles describing their inherent
symmetries. The ensuing factorization of the configuration manifold into a symmetry group …

We study the reduction by symmetry for optimality conditions in optimal control problems of
left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions …

A matrix control algorithm based on controlled Lagrangian method is presented in this paper
to stabilize a class of mechanical systems with underactuation degree one. Firstly, a desired …

We propose a systematic procedure called the Clebsch canonization for obtaining a
canonical Hamiltonian system that is related to a given Lie-Poisson equation via a …

In this paper we study reduction by symmetry for optimality conditions in optimal control
problems of left-invariant affine multi-agent control systems, with partial symmetry breaking …

We consider the problem of stabilizing what we call a pendulum skate, a simple model of a
figure skater developed by Gzenda and Putkaradze. By exploiting the symmetry of the …

We extend the method of controlled Lagrangians with kinetic shaping to those mechanical
systems on semidirect product Lie groups with broken symmetry, more specifically to the …

Motivated by the problem of stabilizing bottom-heavy underwater vehicles, we find the
matching condition for controlled Lagrangians via the kinetic shaping for mechanical …

We extend the method of Controlled Lagrangians to Euler-Poincaré mechanical systems
with broken symmetry, and find asymptotic stabilizing controls of unstable equilibria of such …