Ch 1. Particle General Motion Multimedia Engineering Dynamics Position,Vel & Accel. Accel. varyw/ Time Accel. Constant Rect. Coordinates Norm/Tang. Coordinates Polar Coordinates RelativeMotion
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll

DYNAMICS - THEORY

In many situations, there is a need to examine the motion of two or more points relative to each other.

Consider two points, A and B, both in motion relative to the origin O. This section will examine the motion of B relative to A.

Position

If rB/A is the position vector of B relative to A, then it can be stated that
 rB = rA + rB/A

This is simply adding two position vectors to get a new total vector. This is illustrated in the diagram at the left.

Velocity

To find the relative velocities of two points, take the time derivative of the position, giving

d(rB)/dt = d(rA + rB/A)/dt

 vB = vA + vB/A

Acceleration

Relative acceleration is found by taking the time derivative of the velocity,

d(vB)/dt = d(vA + vB/A)/dt

 aB = aA + aB/A

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