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.
Mathematical model for diamond-type crystals with impurities or defects.
Mathematical models of suspension bridges
In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature...
Mathematical models of suspension bridges: existence of unique solutions
Measure-differential inclusions in percussional dynamics.
Mécanique et géométrie dans les écrits de Mécanique de John Wallis. Le calcul du centre de gravité
John Wallis publie entre 1669 et 1671 les trois parties de son traité de Mécanique, qu’il caractérise lui-même comme un traité de géométrie. La mécanique est située à l’intérieur de la géométrie, dont elle partage les méthodes, puisque les propriétés du mouvement sont démontrées more geometrico. Wallis veut fonder la mécanique sur de nouvelles bases. Pour cela, il y applique une méthode qu’il a élaborée dans l’Arithmetica infinitorum, en partant de la méthode des indivisibles de Cavalieri, et qu’il...
Mechanical Lagrangian systems with external forces.
Mechanical oscillators with dampers defined by implicit constitutive relations
We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...
Mémoire sur la rotation de la lune
Mémoire sur le développement algébrique de la fonction perturbatrice.
Mémoire sur le mouvement vibratoire d'une membrane de forme elliptique.