1. Particle pendulum with air-resistance   (2D dynamics)

The figure to the right shows a particle Q of mass m = 100 kg at the distal end of a straight cable B of length L = 50 m. Earth's local gravitational acceleration is g = 9.8 m/s2. Air-resistance of force   -2*v   resists the pendulum motion. This problem shows how to use MotionGenesis™ to determine the pendulum angle q and cable tension as a function of time. Dynamics: F = m a,   M = I 𝛂,   Lagrange, Kane Program responses Dynamics: With quaternion Program responses To simulate/plot with MATLAB®, edit   MGParticlePendulumDynamics.txt,   and change     ODE() ParticlePendulumDynamics     to     ODE() ParticlePendulumFma.m This causes MotionGenesis™ to auto-generate the file ParticlePendulumFma.m Alternately, use this MotionGenesis™   file   to auto-generate a MATLAB®   .m file   with plant dynamics   (e.g., for Simulink®). Enlarge image

2. Rigid-body pendulum   (2D dynamics)

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The figure to the right shows a non-uniform rigid rod A attached by a frictionless pin joint to Earth N (a Newtonian reference frame). The only external forces on rod A are contact forces at No (the point of N in contact with A) and Earth's gravitational force. Rigid-body pendulum problem statement Student (.pdf) Instructor (.pdf) Dynamics: M = I 𝛂, Lagrange, Kane Program responses Enlarge image

3. Metronome   (2D Dynamics -- Euler, Lagrange, Kane)

Metronome problem statement Student (.pdf) Instructor (.pdf) Form equations of motion with the methods of Euler (angular momentum principle), Lagrange, ... Dynamics: M = I 𝛂, Lagrange, Kane Program responses Video: Metronomes synchronize each other   (B)

4. Helicopter retrieval   (2D variable-length pendulum)   See detailed description.

Helicopter retrieval problem statement (.pdf) Dynamics: F = m a, Kane Program responses

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5. Swinging spring   (2D pendulum, particle on spring)

Swinging spring problem statement (.pdf) Dynamics: F = m a, Lagrange, Kane Program responses

6. Foucault pendulum   (3D motion with spinning Earth)

Foucault-pendulum problem statement (coming soon) (.pdf) Dynamics at North Pole: F = m a, Lagrange, Kane Program responses Dynamics at latitude: F = m a, Lagrange, Kane Program responses

7. Spherical pendulum   (3D tether/wrecking-ball forces & motion)

Spherical-pendulum problem statement (.pdf) Dynamics: F = m a Program responses

8. Tether ball   (2D/3D particle wrapping around a cylinder)

Rigid-body pendulum problem statement Student (.pdf) Instructor (.pdf) 2D: F = ma Program responses 3D: F = m a Program responses

9. Swinging beam on two cables   (construction hoist)

Swinging beam problem statement (.pdf)

10. Trifilar pendulum   (3D aircraft)

Trifilar-pendulum problem statement (.pdf) Statics: F = 0    M = 0 Program responses Statics: Kane augmented Program responses Statics: Kane embedded Program responses Dynamics: F = m a    M = dH/dt Program responses Dynamics: Kane augmented Program responses Dynamics: Kane embedded Program responses Constraints: Yaw/pitch/roll Program responses

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