Kinematics - Linear Velocity


On these pages I have used calculus notation, this is very powerful but may be intimidating if you are not used to this notation. dx/dt means the rate of change of x with t , for more information see:

Uniform Velocity

If an object is moving at a constant speed in the x-direction, without rotation, its motion is given by:

v = dx / dt

or integrating:

x = ∫v dt

In the more general case of translation in 3 dimensions, velocity is a 3 dimensional vector:

= = d / dt

For further information about differentiation see here

Velocity of solid object

Unusually the velocity of a solid body is taken to be the velocity of the centre of mass (explained in the dynamics section). However, the velocity of a solid object could be taken as the velocity of any point on the mass, for example on say the hand of a robot arm, it may be more convenient to use the part of the hand connected to the wrist.

The velocity of any other point on the object will be the objects velocity + and difference due to the objects rotation. If the object is rotating then each particle, which makes up the object, will have a different instantaneous velocity

Modeling velocity using matrices


a(t)= [R(t)]l


In other words, if we take a fixed point on an object, and transform the object by multiplying it with a rotation matrix, which is a function of time, then we will get a vector which is rotating as defined by the matrix.

If we want to get the velocity of this vector then we need to differentiate the matrix t give,

a(t)= [(t)]l


Representing Velocity in program

Velocity in 3D space can be held in a 3D vector (see class sfvec3f). For an example of how this might be used in a scenegraph node, see here.

metadata block
see also:


Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.


cover Engineering Mechanics - Includes Statics book and dynamics book below..

cover Engineering Mechanics Vol 2: Dynamics - Gives theory for rigid dynamics, aims to allow prediction of effects of force and motion. Includes rotating frame of reference. Lots of colour diagrams, I guess its college / University level.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

cover LEGO Mindstorms NXT - Allows you to build a robot and program it from a PC or Mac. Contains an Intelligent Brick with 32-bit microprocessor, memory and FLASH, 3 Interactive Servo motors with built-in rotation sensors, sound sensor, ultrasonic sensor, touch sensor, light sensor, USB 2.0 and Bluetooth support. Icon-based drag-and-drop program "building" environment.

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.