FORCOS

The Forcos function evaluates a Fourier Cosine series at a specific value $x$ .

Format

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

Arguments

$x$: The independent variable. For example, to specify time as the independent variable, specify $x$ as TIME.
$x_{0}$: The shift in the Fourier Cosine series.
$ω$: The fundamental frequency of the Fouries series. It is assumed to be specified in radians per unit of $x$ unless a D is used after the value.
$c_{0}$: The constant bias term.
$c_{1}, c_{2}, \dots, c_{30}$: The coefficients for the Fourier Cosine series.

Definition

(1)

\begin{array}{l} Forcos = c_{0} + \sum_{i = 1}^{N} c_{i} C_{i} (x - x_{0}) \\ where, \\ C_{i} (x - x_{0}) = \cos (i ω (x - x_{0})) and \\ N = Number of terms in the series (N \leq 30) \end{array}

Example

<Motion_Joint
     id                  = "301001"
     label               = "Motion_Joint name"
     type                = "EXPRESSION"
     val_type            = "D"
     expr                = "FORCOS(TIME,0.1,6.28,0.1,0.2)"
     joint_id            = "10003"
     joint_type          = "R"
/>