Analytical Dynamics - Lagrangian and 3D Rigid Body Dynamics

Analytical Dynamics - Lagrangian and 3D Rigid Body Dynamics

Ross Dynamics Lab via YouTube Direct link

Kinematics and Dynamics of a Single Particle | Lecture 1 of a Course

1 of 29

1 of 29

Kinematics and Dynamics of a Single Particle | Lecture 1 of a Course

Class Central Classrooms beta

YouTube playlists curated by Class Central.

Classroom Contents

Analytical Dynamics - Lagrangian and 3D Rigid Body Dynamics

Automatically move to the next video in the Classroom when playback concludes

  1. 1 Kinematics and Dynamics of a Single Particle | Lecture 1 of a Course
  2. 2 Planar kinematics and kinetics of a particle
  3. 3 Rotating and translating frames, linear momentum and angular momentum and their rates of change
  4. 4 Demonstrations of the transport theorem, Matlab demo for mass sliding on parabola
  5. 5 Tetherball dynamics, conservation of angular momentum and central forces
  6. 6 Multi-particle system, center of mass, total linear momentum | center of mass motion | superparticle
  7. 7 Multi-particle system: center-of-mass frame, angular momentum, energy, and applications
  8. 8 Two particle 2D example, rigid body of particles and its kinematics
  9. 9 Moment of inertia tensor/matrix for a rigid body, principal axis frame
  10. 10 Newton-Euler equations for a rigid body | center of mass & inertia tensor calculation worked example
  11. 11 Rotational dynamics about an arbitrary reference point, planar rigid body motion, car jump example
  12. 12 3D rigid body kinematics, rotation matrices & Euler angles, Euler principal axis & angle of rotation
  13. 13 Rigid body kinematic differential equation for Euler angles and rotation matrix
  14. 14 Free Rigid Body Dynamics | Stability About Principal Axes | Qualitative Analysis of Spinning Objects
  15. 15 Torque-free motion of a symmetric rigid body, kinetic energy of a rigid body | caber toss analysis
  16. 16 Free rigid body phase space; spin stabilization of frisbees
  17. 17 Lagrangian mechanics introduction | generalized coordinates, constraints, and degrees of freedom
  18. 18 D’Alembert’s Principle of Virtual Work | active forces and workless constraint forces
  19. 19 Lagrange's equations from D’Alembert’s principle | several worked examples
  20. 20 Lagrange’s equations with conservative and non-conservative forces | phase space introduction
  21. 21 Phase portraits via potential energy | bifurcations | constraint forces via Lagrange multipliers
  22. 22 Lagrange multipliers and constraint forces | nonholonomic constraints | downhill race various shapes
  23. 23 Constants of motion, ignorable coordinates and Routh procedure | spherical pendulum eqns derived
  24. 24 Chaos in mechanical systems, Routh procedure, ignorable coordinates & symmetries | Noether's theorem
  25. 25 Friction and phase portraits | Coulomb friction | cone of friction | falling broom | spinning top
  26. 26 Rolling coin, bicycles, fish, Chaplygin swimmer | small oscillations about equilibrium
  27. 27 Normal modes of mechanical systems
  28. 28 Quasivelocities & dynamic equations | Kane's method, Kane's equations, avoiding Lagrange multipliers
  29. 29 Coupled rigid bodies, impulsive dynamics, applications| trap jaw ants, leaping lizards, falling cat

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.