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