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Program or value
<< PEQ STEQ MINIT NAME LIST MITM MSOLVR >>
"vel. & acc. polar coord."
{ r rD rDD θD θDD vr vθ v ar aθ a }
{ 'vr = rD' 'vθ = r*θD' 'v = √(vr^2 + vθ^2)'
'ar = rDD − r*θD^2' 'aθ = r*θDD + 2*rD*θD'
'a = √(ar^2 + aθ^2)' }
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An explanation of the variables follows:
SOLVEP = a program that triggers the multiple equation solver for the
particular set of equations stored in variable PEQ;
NAME = a variable storing the name of the multiple equation solver, namely,
"vel. & acc. polar coord.";
LIST =
a list of the variable used in the calculations, placed in the order
we want them to show up in the multiple equation solver
environment;
PEQ =
list of equations to be solved, corresponding to the radial and
transverse components of velocity (vr, vθ) and acceleration (ar,
a) in polar coordinates, as well as equations to calculate the
θ
magnitude of the velocity (v) and the acceleration (a) when the
polar components are known.
r, rD, rDD = r (radial coordinate), r-dot (first derivative of r), r-double dot
(second derivative of r).
θD, θDD = θ-dot (first derivative of θ), θ-double dot (second derivative of θ).
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Suppose you are given the following information: r = 2.5, rD = 0.5, rDD = -
1.5, θD = 2.3, θDD = -6.5, and you are asked to find vr, vθ, ar, aθ, v, and a.
Store into variable:
SOLVEP
NAME
LIST
PEQ
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