Kinematics

In physics, kinematics is the branch of mechanics concerned with the motions of objects without being concerned with the forces that cause the motion. In this latter respect it differs from dynamics, which is concerned with the forces that affect motion.

Fundamental equations

Relative motion

This is a simple equation from vector mathematics that restates vector addition: motion of A relative to O is equal to the motion of B relative to O plus the motion of A relative to B:

Related Topics:
Vector - Mathematics

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r_{A/O} = r_{B/O} + r_{A/B} ,!

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Rotating frame

One fundamental equation in kinematics is the equation for the derivative of a vector described in a rotating frame of reference. As a sentence, it is: the time derivative of a vector in a fixed frame is equal to the derivative of the vector relative to the rotating frame plus the cross product of the angular velocity of the frame with the vector. In equation form that is:

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left.rac{dr(t)}{dt} ight|_{X,Y,Z} = left.rac{dr(t)}{dt} ight|_{x,y,z} + omega imes r(t)

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where:

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r(t) is a vector

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X,Y,Z is the fixed frame

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x,y,z is the rotating frame

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ω is the rate of rotation of the frame.

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