Lie algebroids in classical mechanics and optimal control.
Lie point Symmetries of Hamiltonian Systems
Limit cycles in the equation of whirling pendulum with autonomous perturbation
The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.
Limiting phase trajectories and resonance energy transfer in a system of two coupled oscillators.
Lineare invariante Gebilde in äquiformen Bewegungen der Räume endlicher Dimension
Linearization of nonholonomic systems at equilibrium points.
Locally variational invariant field equations and global currents: Chern-Simons theories
We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.
Los Espacios de Hilbert-Lobatschewsky. La masa de un gas relativista. Las ondas relativistas de materia.
LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot with a reaction wheel
A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear...
Lyapunov-based PD linear control of the oscillatory behavior of a nonlinear mechanical system: the inverted physical pendulum with moving mass case.