MotionGenesis: F=ma Software, textbooks, training, consulting.   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 Program responses
Dynamics: Kane/Lagrange Program responses
To simulate/plot with MATLAB®, edit   ParticlePendulumFma.txt,   and
change   ODE() ParticlePendulumFma   to   ODE() ParticlePendulumFma.m
Alternately, use this MotionGenesis™   file   to auto-generate a
MATLAB®   .m file   with plant dynamics   (e.g., for Simulink®).
MotionGenesis Particle pendulum
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MotionGenesis: Particle pendulum angle vs. time
MotionGenesis: Particle pendulum tension vs. time

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*a Program responses
Dynamics: Kane/Lagrange Program responses
MotionGenesis Rigid body pendulum
MotionGenesis: Rigid-body pendulum angle vs. time
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3. Two-particle 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: Euler, Lagrange, Kane Program responses
Video: Metronomes synchronize each other   (B)
MotionGenesis Metronome MotionGenesis Metronome

4. Helicopter retrieval   (2D variable-length pendulum)   See detailed description.
Helicopter retrieval problem statement (.pdf)
Dynamics: F = m*a Program responses
Dynamics: Kane's method Program responses
MotionGenesis Helicopter retrieval MotionGenesis Helicopter retrieval
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5. Swinging spring   (2D pendulum, particle on spring)
Swinging spring problem statement (.pdf)
Dynamics: F = m*a Program responses
Dynamics: Kane/Lagrange Program responses
MotionGenesis Swinging spring MotionGenesis Swinging spring

6. 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
MotionGenesis: Tether ball, wrap particle around cylinder (2D) MotionGenesis: Tether ball, wrap particle around cylinder (3D)

7. Spherical pendulum   (3D tether/wrecking-ball forces & motion)
Spherical-pendulum problem statement (.pdf)
Dynamics: F = m*a Program responses
MotionGenesis Spherical pendulum MotionGenesis Spherical pendulum

8. Swinging beam on two cables   (construction hoist)
Swinging beam problem statement (.pdf)
WindowWasherBeamPublicDomainFromPxHereComCroppedE.jpg
MGBeamOnTwoCablesSchematicSimple.jpg MGBeamOnTwoCablesDynamicsXtDamped.jpg

9. 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
MGAircraftTrifilarPendulum.jpg MGAircraftTrifilarPendulum.jpg