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Analytical mechanics

Also listed as: מכניקה אנליטית

Lagrangian and Hamiltonian mechanics: the reformulation that makes multibody dynamics, robotics and orbital mechanics tractable. It maps to no job title and improves your work in three tracks.

Semester
Not fixed
Weekly hours
3h
Counts as
Department electives
Interest areas
Structures and computational mechanics · Aeronautics and space · Mechatronics and robotics

What it covers

Topics

  • Generalised coordinates and constraints
  • Virtual work and d'Alembert's principle
  • Lagrange's equations
  • Hamilton's principle, Hamiltonian mechanics and the canonical equations
  • Legendre transform
  • Conservation laws and symmetries
  • Small oscillations and normal modes
  • Rigid-body dynamics: Euler angles, Euler equations, spinning tops
  • Introduction to canonical transformations and phase space

Results worth carrying out

  • Lagrange's equations

    ddt ⁣(Lq˙i)Lqi=Qi\frac{d}{dt}\!\left(\frac{\partial L}{\partial \dot{q}_i}\right) - \frac{\partial L}{\partial q_i} = Q_i
  • Hamiltonian

    H=ipiq˙iLH = \sum_i p_i \dot{q}_i - L
  • Euler's rigid-body equations

    I1ω˙1+(I3I2)ω2ω3=M1I_1\dot{\omega}_1 + (I_3 - I_2)\,\omega_2\omega_3 = M_1

Figures worth knowing

  • Phase-space portraits
  • Double-pendulum and spinning-top diagrams

Related courses

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