CHEBY

The Cheby function evaluates a Chebyshev polynomial at a specific value $x$ .

Format

$Cheby (x, x_{0}, c_{0}, c_{1}, \dots, c_{30})$

Arguments

$x$: The independent variable. For example, to specify time as the independent variable, specify $x$ as TIME.
$x_{0}$: The phase shift in the Chebychev polynomial.
$c_{0}, c_{1}, \dots, c_{30}$: The coefficients in the Chebychev polynomial. Specify only as many coefficients as needed with a maximum of 31 coefficients.

Definition

(1)

\begin{array}{l} Cheby = \sum_{i = 0}^{N} c_{i} P_{i} (x - x_{0}) \\ where, \\ P_{i} (x - x_{0}) = 2 (x - x_{0}) P_{i - 1} (x - x_{0}) - P_{i - 2} (x - x_{0}) \\ N = Number of terms in the series (N \leq 30) \\ with, \\ P_{0} (x - x_{0}) = 1 \\ P_{1} (x - x_{0}) = (x - x_{0}) \end{array}

Example

<Force_Vector_TwoBody
     id                    = "30101"
     type                  = "ForceOnly"
     i_marker_id           = "30102031"
     j_floating_marker_id  = "30101031"
     ref_marker_id         = "30101010"
     fx_expression         = BISTOP(DX(30102030,30101010,30101010),
                             VX(30102030,30101010,30101010),0.5,9.5,10000000,2.1,1,0.001)"
     fy_expression         = "0"
     fz_expression         = "0"
  />