List of equations in classical mechanics

Classical mechanics is the branch of physics used to describe the motion of macroscopic objects.

The concepts it covers, such as mass, acceleration, and force, are commonly used and known.

[2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of reference.

The point of concurrency of the three axes is known as the origin of the particular space.

[3] Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another.

These include differential equations, manifolds, Lie groups, and ergodic theory.

(Symbols vary) Discrete masses:

Most of the time we can set r0 = 0 if particles are orbiting about axes intersecting at a common point.

Torque Every conservative force has a potential energy.

By following two principles one can consistently assign a non-relative value to U: where

and p = p(t) are vectors of the generalized coords and momenta, as functions of time In the following rotational definitions, the angle can be any angle about the specified axis of rotation.

= unit vector tangential to the angle.

and the cross-product is a pseudovector i.e. if r and p are reversed in direction (negative), L is not.

For rigid bodies, Newton's 2nd law for rotation takes the same form as for translation:

The precession angular speed of a spinning top is given by:

The mechanical work done by an external agent on a system is equal to the change in kinetic energy of the system: The work done W by an external agent which exerts a force F (at r) and torque τ on an object along a curved path C is:

where θ is the angle of rotation about an axis defined by a unit vector n. The change in kinetic energy for an object initially traveling at speed

For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is

Euler also worked out analogous laws of motion to those of Newton, see Euler's laws of motion.

These extend the scope of Newton's laws to rigid bodies, but are essentially the same as above.

can immediately follow by applying the above definitions.

For any object moving in any path in a plane,

the following general results apply to the particle.

where again m is the mass moment, and the Coriolis force is

For a massive body moving in a central potential due to another object, which depends only on the radial separation between the centers of masses of the two objects, the equation of motion is:

If acceleration is not constant then the general calculus equations above must be used, found by integrating the definitions of position, velocity and acceleration (see above).

For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform.

The situation is similar for relative accelerations.

V = Constant relative velocity between two inertial frames F and F'.

Ω = Constant relative angular velocity between two frames F and F'.