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Chapter
Energy, work and power
In order to use mathematics efficiently to deal with the mechanics of groups of particles, including rigid bodies, it is helpful first to use Newton’s laws to derive other principles. In this chapter, Newton’s...
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Book
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Chapter
Dimensions and bases
Again we consider displacements as a particular example of vectors and, in the first instance, restrict ourselves to displacements in a fixed plane.
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Chapter
Applications of vectors
The results of the preceding chapters are now used in three different circumstances. The principal application to be discussed in this book is the geometry of real space but some elementary kinematical and phy...
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Chapter
The vector product
The vector product (often called the cross product) of two vectors a and b, denoted by a × b, or sometimes a ∧ b, is defined to be a vector of magnitude |a| |b| sin θ, where θ is the angle contained between a and...
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Chapter
An introduction to vectors
In applying mathematics, particularly in the fields of physics and engineering, we need to be able to associate numbers with quantities that are important.
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Chapter
The scalar product
In any triangle ABC, the cosine rule states that
(3.1) <math display='block'> <mrow> <msup> <mi>c</mi> <mn>2</mn> <... -
Chapter
Differentiation and integration of vectors
We have already met vectors which depend on the value of a scalar variable; for example, if r is the position vector of a point on a straight line ...
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Article
A statistical model of the longitudinal dispersion process in turbulent flow in a channel
The important practical problem of the dispersion of a passive contaminant in a fluid flowing through a pipe or channel of uniform cross-section is usually analysed in terms of the distribution of concentratio...
