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Program or value
Store into variable:
<< PEQ STEQ MINIT NAME LIST MITM MSOLVR >>
SOLVEP
"vel. & acc. polar coord."
NAME
{ r rD rDD
θ
D
θ
DD vr v
θ
v ar a
θ
a }
LIST
{ 'vr = rD' 'v
θ
= r*
θ
D' 'v =
√
(vr^2 + v
θ
^2)'
'ar = rDD
−
r*
θ
D^2' 'a
θ
= r*
θ
DD + 2*rD*
θ
D'
'a =
√
(ar^2 + a
θ
^2)'
}
PEQ
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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
,
v
θ
) and acceleration (
ar
,
a
) in polar coordinates, as well as equations to calculate the
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).
θ
D
,
θ
DD
=
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,
θ
D = 2.3,
θ
DD = -6.5, and you are asked to find vr, v
θ
, ar, a
θ
, v, and a.
θ