Classical Dynamics
Table of Contents
Pre-Requisites
Calculus, Multi-Variable Calculus and Basic Physics is assumed. Also it is helpful to know how to solve Differential Equations upto second order.
Topics Covered
Classical Dynamics
- Review of Vectors
- Basics of Vector Algebra
- Basis Vectors
- Scalar and Dot Products
- Summation Convention (Einstein’s Notation)
- Alternating Tensors and Kronecker Delta
- Vector Equation of Planes
- Shifting and Rotating Basis Vectors
- Newtonian Dynamics
- Position, Velocity and Acceleration
- Basic Trajectories
- Polar Co-Ordinate Motion
- Newton’s Laws and Equation of Motion
- Force and Energy
- Angular Momentum and Moments
- Collection of Particles
- Orbital Mechanics
- Lagrangian Mechanics and Calculus of Variations
- Hamiltonian Dynamics
- Poisson Brackets
- Symmetry
- Phase Portraits
Dynamical Systems
- First Order Autonomous Equations
- Fixed Points, Linearization and Flow Diagrams
- Bifurcation Diagrams
- Logistic Equations
- Linear 2-Dimensional Systems
- Classification of Fixed points and Phase Portraits
- Classification Diagram
- Non-Linear 2-Dimensional Systems
- Classification of fixed points
- Linearization Theorem and Linear Stability Analysis
- Null Clines and Phase Portraits
Notes
Classical Dynamics Notes
Lecture Notes
These will be added to the main notes above in due time but the lecture notes below contain all the information.
- Lecture 13: Continuation of Analysis of Spinning Tops using Lagrangian Mechanics
- Lecture 14: Hamiltonian Mechanics and Poission Brackets
- Lecture 15: Continuation of Poission Brackets and Normal Modes
- Lecture 16: Phase Portraits and Symmetry
TODO
- Polish notes and combine Lecture notes to main notes
- Add Dynamical Systems Notes