Classical Mechanics 1

1. Apply vector calculus to solve problems in classical mechanics.
2. Analyze motion under central and conservative forces.
3. Derive and apply Kepler's laws of planetary motion.
4. Model and analyze simple harmonic, damped, and forced oscillations.
5. Apply Lagrangian and Hamiltonian mechanics to solve complex mechanical problems.
6. Understand the concepts of frames of reference and generalized coordinates.

13 weeks, about 45 hours in total. Yours will differ.

1. Week 1Module 1: Motion in Central Force Fields

   • Unit 1: Vector Analysis · 3 hours

     Review vector position, addition, subtraction, and multiplication.. Practice calculating gradients, divergence, and curl.. Solve self-assessment exercises on vector manipulation..

2. Week 2Module 1: Motion in Central Force Fields

   • Unit 2: Central – Conservative Forces · 3 hours

     Define central, conservative, and central-conservative forces.. Study the properties of central force fields and their implications.. Understand the work performed by conservative force fields..

3. Week 3Module 1: Motion in Central Force Fields

   • Unit 3: Kinematics in Polar coordinates · 3 hours

     Learn to transform between Cartesian and polar coordinates.. Evaluate velocity and acceleration components in polar coordinates.. Solve problems involving motion in polar coordinates..

4. Week 4Module 1: Motion in Central Force Fields

   • Unit 4: Energy Conservation in Central – Conservative Force Fields · 3 hours

     Derive the radial energy equation.. Apply energy conservation principles to central conservative force fields.. Solve problems using the radial energy equation..

5. Week 5Module 1: Motion in Central Force Fields

   • Unit 5: Central – Conservative Force and Planetary Motion · 3 hours

     Review Kepler's laws of planetary motion.. Study motion in an inverse square law force field.. Relate Kepler's laws to Newton's laws of gravitation and motion..

6. Week 6Module 2: Oscillatory Motion

   • Unit 1: Linear Simple Harmonic Osillator · 3 hours

     Understand the concept of simple harmonic motion (SHM).. Derive the equation of motion for SHM.. Study examples of SHM, such as a simple pendulum and a mass-spring system..

7. Week 7Module 2: Oscillatory Motion

   • Unit 2: Conservation of Energy in SHM · 3 hours

     Find expressions for kinetic and potential energies in SHM.. Establish that total energy remains constant during SHM.. Solve problems involving energy conservation in SHM..

8. Week 8Module 2: Oscillatory Motion

   • Unit 3: Damped Oscillatory Motion · 3 hours

     Derive the equation of motion for damped oscillatory motion.. Study the effects of damping on SHM.. Distinguish between underdamped, critically damped, and overdamped systems..

9. Week 9Module 2: Oscillatory Motion

   • Unit 4: Forced Oscillatory Motion · 3 hours

     Derive the equation of motion for forced oscillatory motion.. Study the phenomenon of resonance.. Analyze the behavior of systems under external oscillatory forces..

10. Week 10Module 2: Oscillatory Motion

    • Unit 5: Coupled Oscillation · 3 hours

      Establish equations of motion for two coupled oscillatory systems.. Determine normal frequencies and normal modes of vibration.. Solve problems involving coupled oscillations..

11. Week 11Module 3: Lagrange and Hamiltonian Meachanics

    • Unit 1: Frame of Reference and Constraints of Motion · 3 hours

      Distinguish between inertial and non-inertial frames of reference.. Understand how to impose constraints on a system.. Study holonomic and non-holonomic constraints..

12. Week 12Module 3: Lagrange and Hamiltonian Meachanics

    • Unit 2: Generalized Coordinates · 3 hours

      Define generalized coordinates and degrees of freedom.. Derive generalized quantities like velocity, momentum, and force.. Apply generalized coordinates to simplify system analysis..

    • Unit 3: Lagrange's Mechanics · 3 hours

      Understand the importance of generalized coordinates and constrained motion.. Derive Lagrange's equations of motion.. Apply the Lagrange method to solve problems..

13. Week 13Module 3: Lagrange and Hamiltonian Meachanics

    • Unit 4: Hamilton's Mechanics · 3 hours

      Understand the importance of generalized coordinates and constrained motion.. Derive Hamilton's equations of motion.. Apply the Hamilton method to solve problems..

    • Unit 5: Between Newtonian, Lagrangian and Hamiltonian Mechanics · 3 hours

      Transform Newton's law from vector to scalar notation.. Compare Newtonian, Lagrangian, and Hamiltonian mechanics.. Understand the relationships between these three approaches..