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Lagrangian Mechanics Description

Key Elements

Code

MATH 303

Formation

BS Mathematics

Semester

5

Credits

6

Number of Teaching Hours

30

Number of Tutoring Sessions

30

Number of Laboratory Sessions

0

Content

Objective

1. Determine and define the kinematics torsors (speed and acceleration) 2. Determine and define the inertia matrices of a rigid body 3. Determine and define the kinetic and dynamic torsors 4. Write the general theorems and derive the motion equations of a material system. 5. Define the links and write the link equations (holonomic and semi-holonomic) 6. Define the virtual displacement as the virtual work theorem (D'Alembert's principle) and write the Lagrange equations

Content

1. Vector fields:-Torsors-Centerline 2. Kinematics: Review the Kinematic of a material point - rigid body kinematics: rotation vector of a solid body- kinematics of solids in contact. 3. Geometry Mass: Center of mass, moment of inertia, inertia matrix. 4. Kinetics: kinetic torsors, dynamic torsors. 5. Dynamics: Torsors of forces, general theorems, work and power. 6. Links: degree of freedom, Coulomb's law, binding equation (holonomic and non holonomic) 7. Lagrangian mechanics: Virtual moving, D’Alembert theorem, Lagrange equations (with and without multipliers).