Component
École Nationale Supérieure d'Électrotechnique d'Électronique d'Informatique d'Hydraulique et des Télécommunications
Objectives
Be able to easily establish the law of behavior of a complex system using Lagrangian mechanics.
Description
Advantages of Lagrangian mechanics:
It allows the law of behavior of a system to be established by analyzing its energy exchanges with the outside world, unlike Newtonian mechanics, which allows the law of behavior of a system to be established by analyzing the forces applied to each of the solids that compose it. Thus:
- There is no need to manipulate all the forces that do not exchange energy with the system, such as connection forces. This simplifies the study of complex systems with a large number of solids (and therefore connections).
- The energy-based approach allows multiphysical systems to be handled.
- It is a scalar (energy) approach rather than a vector (force) approach.
- There is no longer any need to isolate each solid.
Course content: (6 lecture slots, 1 tutorial slot)
- Review of the main concepts of mechanics (reference frames, forces, moments, kinematic connections, etc.).
- Review of the principles of Newtonian mechanics (PFD).
- Presentation of concepts used in Lagrangian mechanics (mobility of a system, generalized coordinates, energies).
- Presentation of Lagrangian mechanics equations based on Newtonian mechanics equations.
- Presentation of the concept of virtual mobility.
- Adjustment of equations to address electromechanical issues.