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Dynamique du solide rigide

General informations


Ingénieur (niveau M1)

Ingénierie Mécanique







GUERIN Jean-Dominique
kinematics, kinématics joints, kinetic and dynamic torsor, equations of Lagrange, virtual work

Pedagogic informations

Training objectives

This course is an introduction to energy methods.
After a review of Newtonian dynamics of a problem description, the Lagrangian description of the problem is dealt, the method of virtual work is applied.
The highly applicative approach of the course allows the student to make the connection between the Newtonian description and the Lagrangian description of a dynamic problem.
With simple case, the student will learn to establish the equations describing the problem, to determine the Lagrangian of the problem, and to identify the distribution of loads.
This approach is used in a preliminary study to characterize the loads acting on rigid considered parts of a mechanism.

Learning objectives
To teach the student to tackle a problem of dynamics of rigid solid by the Lagrangian method to characterize the stresses acting on rigid considered parts of a mechanism.
These same loads are used as data to the dimensioning of deformable parts.

Learning context

Course materials
Handouts of the lessons and training exercises


Course content

Chapter 1: Review
• Kinematics of rigid body : Velocity field, acceleration field,
• Velocities decomposition, accelerations decomposition
• links Notions (holonomic, non-holonomic, semi-holonomic)
• kinematic Torsor and efforts of links Torsor
• kinetic and dynamic Torsors
• Kinetic energy
o Application exercises

Chapter 2: Principles of work (powers) virtual
• virtual differential and derived notions
• Concepts and definitions of virtual Moving and speed
• Virtual Work and power
o Application exercises

Chapter 3: Lagrange equations
• Lagrangian formalism: generalized coordinates, Lagrange multipliers
• Lagrangian equations (conservative system)
o Application exercises

Chapter 4: Application of the equations of Lagrange PPV
• Lagrange multipliers
o Application exercises

Personal work

Label (French) Label (English)
Dynamique du solide rigide Dynamics of rigid bodies

Exam description
written exam

Exam structure