Mechanics §
Overview §
Mechanics models objects whose motion is predictable from position, velocity, forces, and constraints. It is relevant when quantum effects and relativistic speed are negligible: machines, orbits, structures, vehicles, and many engineering systems.
Authoritative sources
History §
- 1687: Newton gives laws of motion and universal gravitation.
- 1736: Euler develops rigid-body dynamics.
- 1788: Lagrange introduces coordinate-based analytical mechanics.
- 1830s: Hamilton gives variational formulations and phase-space methods.
Classification §
| Page | Central question | Typical objects | Main tool |
|---|---|---|---|
| Kinematics | How is motion described? | Particles, trajectories | Position, velocity, acceleration |
| Dynamics | How do forces determine motion, and when is it in equilibrium? | Particles, projectiles, beams, frames | Newton's laws, Lagrangian/Hamiltonian formulations |
| Oscillations and Waves | How do systems repeat motion or propagate disturbances? | Spring-mass systems, pendulums, sound, water waves | Restoring force, natural frequency, wave equation |
| Rigid-Body Mechanics | How do extended bodies rotate and translate? | Robots, wheels, gyroscopes | Inertia tensor, angular momentum, Euler's equations |
| Continuum Mechanics | How do deformable bodies and fluids respond to stress? | Elastomers, fluids, beams, shells | Stress–strain relations, conservation of mass and momentum |
Details
Kinematics provides the language (position, velocity, acceleration) without asking why motion occurs. Dynamics adds the causal layer: forces produce acceleration, and the special case of zero acceleration is static equilibrium. The Lagrangian and Hamiltonian reformulations of dynamics (generalized coordinates, Noether’s theorem, phase space) are treated inside the Dynamics page. Oscillations and Waves extend the equilibrium analysis to periodic and propagating solutions. Rigid-Body Mechanics handles extended bodies that do not deform, while Continuum Mechanics handles bodies that do.