Point and solid mechanics [SMATB208]

Learning outcomes

The objective is to establish i(n a mathematical formalism) the fundamental equations of motion of the mechanics, both in Newtonian and Lagrangian formalisms, first for a point mass, second for a rigid body.

Objectives

To give an overview of the difficulty of solving Newton's equations completely : the use of the first integrals, the distinction betwen external forces and constraints, diagrams of energy, linearization, local solutions, for the point and the solid. 

Content

The course starts with the composition of the velocities and accelerations, in rotating and inertial frames; the case of the rotation of the Earth is presented as example.
The conservation laws are summarized in the classical context of external forces. Diagrams of energy are built in the one-dimensional case.
The introduction of generalized coordinates, virtual displacements, contact forces allows to formulate the motion in a Lagrangian formulation and to revisit the first integrals of motion. Numerous examples are given, in particular the two body problem.
The same laws are rewritten for a rigid body, with the inertia matrix and gyroscopic applications;

Table of contents

- velocities and accelerations

- first integrals

- constraints and virtual deplacements

- Lagrange formalism

- dynamics of a solid

- Lagrange formulation for the solid 

Exercises description

every week, in parallel with the course