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References

Kaufman, H., I. Barkana, and K. Sobel, 1998; Direct Adaptive Control Algorithms Theory and Applications, Springer Verlag, Berlin. ISBN 0-387-94884-8

McKerrow, J.P., 1991; Introduction to Robotics, Addison-Wesley, Sydney, ISBN 0-201-18240-8

Table 1
F(t) ${\mathcal{L}}\{F(t)\}$
1 $\frac{1}{s}$ $s > 0$
$t$ $\frac{1}{s^2}$ $s > 0$
$t^n$ $\frac{n!}{s^{n+1}}$ $s > 0$
$e^{at}$ $\frac{1}{s - a}$ $s > 0$
$\sin{at}$ $\frac{a}{s^2 + a^2}$ $s > 0$
$\cos{at}$ $\frac{s}{s^2 + a^2}$ $s > 0$
$\sinh{at}$ $\frac{a}{s^2 - a^2}$ $s > 0$
$\cosh{at}$ $\frac{s}{s^2 - a^2}$ $s > 0$

Table 2.
${\mathcal{L}}\{F(t)\}$ $f(s)$
${\mathcal{L}}\{F(at)\}$ $\frac{1}{a}f(\frac{s}{a})$
${\mathcal{L}}\{c_1 F_1(t) + c_2 F_2(t)\}$ $c_1 f_1(s) + c_2 f_2(s)$
${\mathcal{L}}\{F'(t)\}$ $s f(s) - F(0)$
${\mathcal{L}}\{e^{at}F(t)\}$ $f(s-a)$
${\mathcal{L}}\{F(t-a)\}$ $e^{-as}f(s)$
${\mathcal{L}}\{\int_0^tF(u) du\}$ $\frac{f(s)}{s}$



Skip Carter 2008-08-20