The Probem of Motion and the Methods to Solve It to be a Great Amateur Theoretical Physicist

This course develops the Newtonian theory of mechanics, it also develops relevant ideas from calculus, linear algebra, multivariable calculus, and ordinary differential equations. Along the way I will also introduce Mathematica and how to use it to solve problems in mechanics (such sections are optional for those who have Mathematica).

For what follows these are good resources:

If you wish to buy a book, I recommend these:

This requires either Mathematica 8 or later, or the free Mathematica CDF Viewer, though the viewer cannot run the programs, (you can find that here). You will also need to download the MAST Writing Style into the folder SystemFiles/Front End/Stylesheets. You can download that here. Once you load this file into the folder rename it MAST Writing Style 3. Reload Mathematica and it will be there.

I am assuming that you have completed studying all of Basic Mathematics and Physics and possibly Basic Ideas of Mathematica.

  1. The Problem of Motion
  2. Review of Dynamical Systems
  3. Review of Motion in One Dimension
  4. Review of Vectors
  5. Characterizing the State Space of Classical Mechanics
  6. Calculus of Vector Functions of a Scalar Variable
  7. Kinematics in More Than One Dimension
  8. General Orthogonal Curvilinear Coordinates
  9. The Kinematical Equations of Motion
  10. Galilean Relativity
  11. Forces and Mass
  12. Forces in Equilibrium
  13. The Program of Newtonian Classical Mechanics
  14. Setting Up Newton's Equation of Motion in More Than One Dimension
  15. Solving Newton's Equations of Motion
  16. Curves in Space
  17. Scalar-Valued Functions of Many Variables and Partial Derivatives
  18. Line Integrals
  19. Work and Power
  20. Kinetic Energy
  21. Potential Energy and Force
  22. Equilibrium
  23. The Harmonic Oscillator
  24. Damping and Forcing of Oscillations
  25. The Conservation of Energy
  26. Virtual Displacement and Virtual Work
  27. Systems of More Than One Particle
  28. The Calculus of Variations
  29. The Principle of Stationary Action
  30. The Euler-Lagrange Equation
  31. Translation Invariance and Momentum Conservation
  32. Accretion and Decay
  33. Collisions and Scattering
  34. Rotation Invariance and Conservation of Angular Momentum
  35. Motion in Accelerated Frames
  36. Rotating Systems
  37. Rigid Bodies
  38. Tensor Algebra
  39. Moment of Inertia
  40. Gyrodynamics

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