Physics Lournal

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Part of Lagrangian Mechanics

Newtonian Mechanics presents the motion of systems as comprised of the positions, velocities, and accelerations, of each component of the system.

The variational perspective describes the system in terms of aggregate properties of the system, such as the total energy.

The Newtonian perspective allows for forces to be described as derivatives of the energy potentials of the system.

The variational perspective presents the equations of motion (the dynamical laws governing the evolution of some physical system), in terms of the difference in kinetic and potential energy.

The potential energy is a number representing the arrangement of components of a system, whereas the kinetic energy represents the velocities of said components.

Referenced in

On The Tension Between Mathematics and Physics

The Principle Of Superposition

An atomic system is comprised of particles (bodies with specific properties of Mass, Inertia), and subject to the laws governing forces acting upon objects. Each component of this system will have various possible motions it could take, and each motion is considered a state. Classically, one can describe this state via the coordinates of the system and the velocities of the components at some point in time, with the complete motion thus being determined.

Lagrangian Mechanics