Flatness of Mechanical Systems with 3 Degrees of Freedom

Control of Mechanical Systems with Variable Degrees of Freedom

Many mechanical systems can change dimension. r θ l k/2 k/2 y v u v m φ Body 2 1 m v v θ Rake x l θ We are primarily concerned with the problem of determining controllability and the motion planning problem. Slide 1 This motivational slide is intended to illustrate two main points: • Changing dimensions is common, and • There is a natural kinematic/dynamic dichotomy in such problems, which will...

Dynamical Systems with Two Degrees of Freedom.

Canonical Gibbs Distribution and Thermodynamics of Mechanical Systems with a Finite Number of Degrees of Freedom

Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of n weakly interacting identical subsystems and passage to the limit n → ∞. In the presented work we develop another approach to these problems assuming that n is fixed and n ≥ 2. The ergodic hypothesis (which frequently is...

Control of Underactuated Mechanical Systems with two Degrees of Freedom and Symmetry

In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained from the Lagrangian of the system that transforms the system into a partially linear cascade non...

Control of Mechanical Systems with Variable Degrees of Freedom Slide 0 Introduction and Motivation

Many mechanical systems can change dimension. r θ l k/2 k/2 y v u v m φ Body 2 1 m v v θ Rake θ l x We are primarily concerned with the problem of determining controllability and the motion planning problem. Slide 1 This motivational slide is intended to illustrate two main points: Changing dimensions is common, and There is a natural kinematic/dynamic dichotomy in such problems, which will be ...