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CHEBY

The CHEBY function evaluates a Chebyshev polynomial at a user specified value x.

Format

CHEBY (x, x0, a0, a1,..., a30)

Arguments

 
x
An expression that specifies the independent variable. For example, if the independent variable in the function is time, x is the system variable TIME.
x0
The phase shift in the Chebyshev polynomial.
a0, a1,..., a30
The coefficients for the Chebyshev polynomial. A maximum of thirty-one coefficients may be specified.

Extended Definition

The CHEBY function evaluates a Chebyshev polynomial at a user specified value x. x0, a0, a1,..., a30 are parameters used to define the constants for the Chebyshev polynomial. The Chebyshev polynomial is defined as:
C(x) = aj Tj (x-x0)
where the functions Tj are recursively defined as:
Tj (x-x0) = 2 * (x-x0) * Tj-1 (x-x0) - Tj-2 (x-x0)
with T0 (x-x0) = 1, and T1 (x-x0) =x-x0.
The index “j” has a range from zero to “n”, where “n” is the number of terms in the series.
Note the following:
T2 (x-x0) = 2 * (x-x0)2 - 1
T3 (x-x0) = 4 * (x-x0)3 - 3 * (x-x0)

Examples

MOTION/1, JOINT=21, TRANSLATION,
,FUNCTION = IF (TIME-2:CHEBY(TIME, 1, 1, 0, -1), 0, 0)
This MOTION statement defines a motion using a quadratic Chebyshev polynomial and the system variable TIME. The arithmetic IF ensures that the function remains zero after 2 time units. When time is less than 2 time units, Adams Solver (C++) evaluates a Chebyshev polynomial to determine the motion. The polynomial defined in the above example is:
Cheby = 1 + 0 * (time-1) - 1 * [2 (time-1)2 - 1]= -2*time2 +4*time
See other Miscellaneous Adams intrinsic functions available.