Classical Mechanics

Momentum
Momentum in classical mechanics If an object is moving in any reference frame, then it has momentum in that frame.The amount of momentum that an object has depends on two physical quantities: th...

Newtons second law of motion
Newton's second law: Law of Motion The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction. Newton's second law as originally state...

Point kinetics in a fixed coordinate system
DefinitioThe position the velocity and the acceleration are defined by:The following holds:When the acceleration is cotant this gives: For the unit vecto in a direction perpen...

Point dynamics in a fixed coordinate system
Force, (angular)momentum and energy Newton's 2nd law connects the force on an object and the resulting acceleration of the object where the momentum is given by ::Newton's 3rd law is given by...

Point dynamics in a moving coordinate system
Apparent forces The total force in a moving coordinate system can be found by subtracting the apparent forces from the forces working in the reference frame: . The different apparent forces are give...

Dynamics of masspoint collections
The centre of mass The velocity with respect to the centre of mass is given by The coordinates of the centre of mass are given by:In a 2-particle system, the coordinates of the centre of mas...

Dynamics of rigid bodies
Moment of Inertia The angular momentum in a moving coordinate system is given by:where I is the moment of inertia with respect to a central axis, which is given by:or, in the continuou...

Variational Calculus
Starting with: the equatio of Lagrange can be derived: When there are additional conditio applying to the variational problem = 0 of the...

Coordinate Systems
The coordinate system is illustrated in Figure below. The location of a pointin three dimeional space may be specified by an ordered set of numbe(x, y, z). The ranges for the coordinate paramete a...