Prerequisites: Vector Spaces (Linear Algebra)

An introduction to differentiable manifolds, tangent ff vectors, vector fields, co vector fields, immersions and submersions, Lie groups, actions of groups, Lie algebras, adjoint co‐adjoint maps, symmetries. Vector fields, integral curves, push‐forward and pull‐back, differential forms and Riemannian geometry.

Euler Poincare reduction for the rigid body and heavy top, satellite dynamics and control with coordinate free models, inverted pendulum on a cart.

Same as Reference

1. Geometric Mechanics and Symmetry, D.D. Holm, T. Schmah and C. Stoica,Oxford University Press, 2009.
2. Introduction to Mechanics and Symmetry, J. Marsden and T. Ratiu, Springer‐Verlag, 1994.
3. Control Theory from the Geometric Viewpoint, Agrachev and Y. Sachkov, Springer, 2004.
4. An Introduction to Manifolds, L. W. Tu, Springer 2008.
5. Ordinary Differential Equations, V. Arnold, Springer, 1992.
6. Elementary Topics in Differential Geometry, J. A. Thorpe, Springer 2004.
7. A Comprehensive Introduction to Differential Geometry, M. Spivak, Publish or Perish, 1999.