CM · Classical mechanics

A planet accelerates even when its speed is constant: velocity includes direction.

Prerequisites: 47.

• Apply Newtonian, Lagrangian 拉格朗日量 and Hamiltonian descriptions
• Analyse rotation, central forces and oscillations
• Use conservation laws with their conditions

Newton’s second law is a vector statement. Choose coordinates and identify constraints before components.

Energy conservation applies when work from nonconservative forces is accounted for; momentum conservation needs zero net external impulse.

For small oscillations, linearise around a stable equilibrium. A restoring term proportional to displacement gives harmonic motion.

Lagrange’s equations use L=T−V and generalised coordinates. This undergraduate formalism is distinct from school-level force substitution.

Choose an inertial frame and a coordinate x measured from spring equilibrium. For a conservative spring, the Lagrangian avoids solving constraint forces.

With m = 2.0 kg and k = 18 N/m, Positive stiffness gives stable motion. The units of k/m are inverse seconds squared.

Conservation of kinetic energy does not hold in every collision, even when momentum is conserved.

Lagrangian: Kinetic energy minus potential energy for the standard mechanical system.

angular momentum 角动量: The moment of linear momentum about a reference point.