Introduction to the Lie symmetries

• The importance of Lie symmetries and their uses;

• Objectives of the course;

• Infinitesimal transformations;

• Infinitesimal generators;

• Prolongations and their generators;

• Lie theorem;

• Order reduction.

Computation of the Lie symmetries for mechanical systems

• Modeling of mechanical systems;

• How to obtain the Lie symmetries of mechanical systems;

• Application of the Lie theorem.

Resolution of mechanical systems via Lie symmetries

• Reduction of order;

• Change of variables;

• Analytical solution;

• Interpretation of the physical meaning of the infinitesimal generators.

Use of the Maple software in the context of the Lie symmetries

• Basic commands;

• Libraries used for Lie symmetries use;

• Infinitesimal transformation;

• Infinitesimal generators;

• Prolongation of the transformations and their generators;

• Lie theorem;

• Order reduction.