Function: math[rotation] - tool to explore bodies of rotation
Calling Sequence:
rotation(f, x=a .. b, axis, object)
Parameters:
f -
expression in x
x -
a name
a, b -
interval boundary points
axis -
axis of rotation, either 'xaxis' or 'yaxis'
object -
property, either 'area', 'volume', 'center' or 'moment'
Description:
The function determines the volume, surface area, center of gravity, or mass moment of inertia of a body of rotation.
f must be a real-valued function in x. The interval boundary points a, b may be numeric or symbolic.
The obligatory third and fourth arguments specify the axis of rotation:
'xaxis'
- rotation about the x-axis,
'yxis'
- rotation about the y-axis,
and the property of the body of rotation you would like to compute:
'area'
-
surface area of the body,
'volume'
- volume of the body (or 'vol' for short), (Rotationsvolumen)
'center'
- center of gravity,
'moment'
- mass moment of inertia
With the optional fifth argument 'floats' or 'float' this function returns the result as a floating-point number using evalf .
If this function returns an undetermined definite integral use function evalf to evaluate it numerically.
This function is part of the math package, and so can be used only after performing the command with(math) or with(math, rotation).
Examples:
> with(math, rotation):
> assume(r, positive):
> rotation(sqrt(r^2-x^2), x=0 .. r, area, xaxis);
> rotation(sqrt(x), x=0 .. 4, area, yaxis);
> rotation(x^2, x=0 .. sqrt(2), vol, yaxis);
> rotation(x*exp(-x), x=0 .. 1, vol, xaxis, float);
> rotation(sqrt(4-x), x=0 .. 4, xaxis, center);
> rotation((4-x)*sqrt(2*x), x=0 .. 4, xaxis, moment, float);
See Also:
math/arclen .
Version History:
Version 1.0 as of November 15, 1997