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dynamics-expert

Expert-level dynamics covering kinematics and kinetics of particles and rigid bodies, Newton-Euler equations, energy methods, impulse-momentum, and vibrations.

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luokai0/ai-agent-skills-by-luo-kai

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Dynamics Expert

Before Starting

  1. Particle or rigid body?
  2. Kinematics or kinetics?
  3. 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

PitfallFix
Non-inertial reference frame in Newton lawTransform to inertial frame first
Wrong mass moment of inertiaUse parallel axis theorem when rotating about non-centroidal axis
Sign error in impact problemsDefine positive directions consistently before and after impact
Ignoring constraint forces in energy methodsConstraint forces do no work in ideal joints

Related Skills

  • statics-expert
  • mechanics-of-materials-expert
  • vibrations-expert

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