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Theoretical physics I (Classical mechanics)


  • Newtonian mechanics
    • Newton's axioms and their consequences
      • Newton's first axiom
      • Newton's second axiom
      • Conservation laws
        • Momentum conservation
        • Angular momentum conservation
        • Energy conservation
      • Newton's third axiom
    • One-dimensional motion
      • General problem
      • Motion in a conservative force field
      • Motion in a gravitational potential (one-dimensional)
      • Motion in a force field depending only on velocity
    • One-dimensional harmonic oscillator
      • Undamped motion
      • Damped harmonic oscillator
      • Driven harmonic oscillator
      • Response to a delta force
      • Green function
    • Two-body problem and motion in a central field
      • Reduction of the two-body problem
      • Relative motion
      • Kepler problem
    • Harmonic oscillations of a system of point masses
      • Harmonic approximation for a system of point masses
      • Eigenmodes
      • Example: the vibrating triangle
      • The vibrating string
    • Rigid body
      • Momentum of inertia tensor
      • Kinetic and potential energy
      • Euler equations
  • Analytical mechanics
    • Lagrange equations of the first kind
      • Constraints
      • Virtual displacements and d'Alembert's principle
      • Method of Lagrange multipliers
    • Lagrange equations of the second kind
      • Generalized coordinates
      • Lagrange equations of the second kind
      • Cyclic coordinates and generalized momenta
      • Elektromagnetic forces
      • Dissipative forces
      • Hamilton's principle
      • Guage transformations
      • Noether's theorem
    • Hamilton formalism
      • Legendre transformation
      • Hamilton's equations of motion
      • Canonical transformations
      • Poisson bracket
  • Special relativity
    • Minkowski space-time
      • Principle of relativity
      • Lorentz transformation
      • Length contraction and time dilation
      • Four-vectors and Lorentz transformation
    • Relativistic mechanics
      • Four-velocity and four-momentum
      • Four-force
      • Relativistic energy
      • Hyperbolic motion