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  • 8:13 PM, Monday, 18 Oct 2021


Course Postgraduate
Semester Electives
Subject Code AVC868
Subject Title Geometric Approach to Mechanics and Control

Syllabus

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.

Text Books

Same as Reference

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