Classical and Computational Mechanics

The course gives an introduction to analytical mechanics, variational principles, dynamics in accelerated coordinate systems and conservation laws.

Particular attention is paid to variational calculus, rigid bodies, dynamics for bodies subject to central forces, accelerated coordinate systems, forced and damped oscillations, nonlinear dynamics and canonical transformations to find conservation laws. The course also includes a brief introduction to discrete Lagrangian variations and Hamiltonian (symplectic) numerical methods for differential equations.

The course lays the basis for further specialisation in mechanics and dynamical systems.

After completion of the course, the student is expected to be able to:

• Explain elementary principles of analytical mechanics, like generalised coordinates, virtual work and variational principle.
• Use variational calculus on simple problems with constraints.
• Use the Lagrange and Hamilton formalism to find the motion equations for simple mechanical systems.
• Describe different types of trajectories for a particle in a central force field, using energy arguments.
• Define the Inertia tensor and derive the motion equations for rigid bodies.
• Describe how to use the Legendre transformation to transform between Lagrangian and Hamiltonian description of mechanics.
• Identify cyclic variables and derive conservation laws for simple Hamiltonian systems using canonical transformations.
• Have a basic knowledge of discrete variations and symplectic numerical methods