luokai0 Dynamics Expert
Before Starting
- Particle or rigid body?
- Kinematics or kinetics?
- Translation, rotation, or general plane motion?
Core Expertise Areas
Kinematics
Particle kinematics: position, velocity, acceleration as functions of time. Projectile motion: independent horizontal and vertical motions under gravity. Relative motion: velocity and acceleration of one point relative to another. Rigid body rotation: v = omega cross r, a = alpha cross r minus omega squared r. General plane motion: translation of reference point plus rotation about it.
Kinetics of Particles
Newton second law: F = ma, vector equation in inertial frame. Work-energy: work done equals change in kinetic energy. Impulse-momentum: integral of F dt equals change in linear momentum. Impact: coefficient of restitution relates velocities before and after collision.
Kinetics of Rigid Bodies
Translation: F = m times a of center of mass. Rotation about fixed axis: M = I alpha, moment equation about axis. General plane motion: F = m times a_cm and M_cm = I_cm times alpha. Angular momentum: H = I omega, conserved without external moments.
Vibrations
Free vibration: x double-dot plus omega_n squared x = 0, solution is sinusoidal. Natural frequency: omega_n = sqrt of k over m for spring-mass system. Damped vibration: damping ratio zeta determines response type. Forced vibration: resonance when excitation frequency equals natural frequency. Transmissibility: ratio of transmitted to applied force in vibration isolation.
Best Practices
- Clearly identify reference frame before writing kinematic equations
- Use energy methods when forces are conservative for simpler solution
- Check units throughout calculation
- Draw velocity and acceleration diagrams for complex mechanisms
Common Pitfalls
| Pitfall | Fix |
|---|---|
| Non-inertial reference frame in Newton law | Transform to inertial frame first |
| Wrong mass moment of inertia | Use parallel axis theorem when rotating about non-centroidal axis |
| Sign error in impact problems | Define positive directions consistently before and after impact |
| Ignoring constraint forces in energy methods | Constraint forces do no work in ideal joints |
Related Skills
- statics-expert
- mechanics-of-materials-expert
- vibrations-expert