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.
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.
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;
- velocities and accelerations
- first integrals
- constraints and virtual deplacements
- Lagrange formalism
- dynamics of a solid
- Lagrange formulation for the solid
every week, in parallel with the course
The exam is separated in two parts : a short oral, with a synthesis to present, after 10 minutes of preparation, and a long written part, with 3 or 4 exercises.
The final mark is the arithmetic average of the marks of both parts, if they have been presented at least once during the academic year and if they are both higher than 7/20. If it is not the case, the final mark will be the lowest one.
Syllabus