SICM Workbook
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Chapter 1 - Lagrangian Mechanics
Notes
- Section 1.6 : How to Find Lagrangians
- Section 1.6.1: Coordinate Transformations
- Section 1.6.2: Systems with Rigid Constraints
- Section 1.8.3: Central Forces in Three Dimensions
- Section 1.8.4: The Restricted Three Body Problem
- Section 1.8.5: Noether's Theorem
- Section 1.9: Abstraction of Path Functions
- Section 1.10 : Constrained Motion
- Section 1.10.1: Coordinate Constraints
- Section 1.10.2: Derivative Constraints
- Section 1.10.3: Non-holonomic Constraints
- Section 1.11: Summary
Exercises
- Exercise 1.11: Kepler's Third Law
- Exercise 1.12: Lagrange's Equations
- Exercise 1.13: Higher-derivative Lagrangians
- Exercise 1.14: Coordinate-independence of Lagrange Equations
- Exercise 1.15: Equivalence
- Exercise 1.16: Central force motion
- Exercise 1.17: Bead on a helical wire
- Exercise 1.18: Bead on a triaxial surface
- Exercise 1.19: Two-bar linkage
- Exercise 1.20: Sliding pendulum
- Exercise 1.21: A dumbbell
- Exercise 1.36: Noether integral
- Exercise 1.37: Velocity transformation
- Exercise 1.38: Properties of ℰ, the Euler Lagrange Operator
- Exercise 1.39: Combining Lagrangians
- Exercise 1.40: Bead on a triaxial surface (incomplete)
Chapter 2 - Rigid Bodies
Notes
- Section 2.1: Rotational Kinetic Energy
- Section 2.2: Kinematics of Rotation
- Section 2.3: Moments of Inertia
- Section 2.4: Inertia Tensor
- Section 2.5: Principal Moments of Inertia
- Section 2.6: Vector Angular Momentum
- Section 2.7: Euler Angles
- Section 2.8 : Motion of a Free Rigid Body
- Section 2.8.1: Computing the Motion of Free Rigid Bodies (incomplete)
- Section 2.8.2: Qualitative Features of Free Rigid Body Motion
- Section 2.9: Euler's Equations
- Section 2.11.1: Spin-Orbit Coupling - Development of Potential Energy
- Section 2.12: Nonsingular Coordinates and Quaternions
Exercises
- Exercise 2.1: Rotational kinetic energy
- Exercise 2.2: Steiner's Theorem
- Exercise 2.3: Some useful moments of inertia
- Exercise 2.4: Jupiter
- Exercise 2.5: A constraint on the moments of inertia
- Exercise 2.6: Principal moments of inertia
- Exercise 2.8: Rotational angular momentum
- Exercise 2.9: Euler angles
- Exercise 2.10: Uniformly accelerated rigid body
- Exercise 2.11: Conservation of Angular Momentum
- Exercise 2.12: Derivation of Euler Angle Kinematics
- Exercise 2.13: Bicycle Wheel (incomplete)