# ELLVEL is the jEllipse module of jLab.

```  ELLVEL  Average and instantaneous ellipse velocities.

V=ELLVEL(KAPPA,LAMBDA,THETA,PHI,STR) where KAPPA and LAMBDA are the
amplitude and linearity of a time-varying ellise, THETA is its time-
varying orientation, and PHI is its time-varying phase, returns various
measures of the ellipse 'velocity'.

STR determines the velocity quantity to be output.

STR       Symbol     Description
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'geo'      VM         Geometric mean velocity
'ave'      VBAR       Period-averaged speed
'kin'      VEKE       Kinetic energy velocity
'cir'      VGAMMA     Circulation velocity
'azi'      VAZ        Instantaneous azimuthal velocity
'ins'      VI         Instantaneous speed

All are signed quantities reflecting the direction of motion.  That is,
a velocity is defined to be positive when the ellipse is orbited in the
mathematically positive (counterclockwise) sense, and negative when the
ellipse is orbited in the mathematically negative sense.

VM=ELLVEL(KAPPA,LAMBDA,THETA,PHI) with STR omitted returns VM, the
geometric mean velocity.  This is a basic of ellipse velocity that is
analagous to the geometric mean radius as a measure of ellipse size.

ELLVEL(DT,...,) optionally uses DT as the data sample rate, with a
default value of DT=1.  DT is a scalar.

ELLVEL(DT,...,FACT,STR) optionally converts the physical units of
velocity through a multiplication by FACT, with a default value of
FACT=1.  For example, FACT=1e5 converts kilometers into centimeters,
while FACT=1e5/24/3600 converts km/day into cm/sec.
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Cell array input/output

If ELLVEL is given cell array input, it returns cell array output.

Thus KAPPA, LAMBDA, THETA, and PHI may each be cell arrays of the
same size, where each element in the cell array is a numerical array.

VM and other velocity measures will be also cell arrays of this size.

In this case ELLVEL(DT,...) also works with DT a scalar or an
array whose length is the number of elements in the cell arrays.
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