Newtonian vs Lagrangian Views of Simple Harmonic Motion
SimpleHarmonicMotion NewtonianMechanics LagrangianMechanics
02:30 Abide by Reason contrasts Newtonian and Lagrangian formulations for students who know (F=ma) and springs but not why we’d switch to energies and Lagrangians.
Lagrangian as Kinetic Minus Potential and Its Energy-Space Geometry
Lagrangian EnergySpace KMinusU
08:30 This note is for learners puzzled by the seemingly arbitrary definition (L = T - U) and wanting a more intuitive picture.
Action as Area Under Lagrangian and Principle of Least Action
Action LeastAction EulerLagrange
13:00 Abide by Reason clarifies the meaning of action for students who have seen (S = \int L,dt) but lack a geometric picture.
Advantages of Lagrangian Mechanics Over Force-Based Newtonian Methods
LagrangianAdvantages GeneralizedCoordinates Constraints
18:00 This note targets learners deciding when to use Newton’s vector-force equations and when to switch to a Lagrangian formulation.
Relationship Between Lagrangian and Hamiltonian Descriptions of Mechanics
HamiltonianMechanics EnergyConservation PhaseSpace
22:00 Abide by Reason briefly contrasts Lagrangian and Hamiltonian mechanics for viewers progressing from configuration-space to phase-space formulations.