[rychlik@ruby ~]$ maxima
GCL (GNU Common Lisp)  Version(2.4.0) Sun Sep 22 00:12:12 MST 2002
Licensed under GNU Library General Public License
Contains Enhancements by W. Schelter
Maxima 5.6 Tue May 21 11:08:32 MST 2002 (with enhancements by W. Schelter).
Licensed under the GNU Public License (see file COPYING)
(C1) theta: omega*t;

(D1) 				    omega t
(C2) s: r * cos(theta) + sqrt(d^2-r^2*sin(theta)^2);

		       2    2	 2
(D2) 		 SQRT(d  - r  SIN (omega t)) + r COS(omega t)
(C3) diff(s,t, 2);

	    2  2    2			  2  2	  2
       omega  r  SIN (omega t)	     omega  r  COS (omega t)
(D3) --------------------------- - ---------------------------
	   2    2    2			 2    2	   2
     SQRT(d  - r  SIN (omega t))   SQRT(d  - r  SIN (omega t))

		       2  4    2	     2
		  omega  r  COS (omega t) SIN (omega t)	       2
	        - ------------------------------------- - omega  r COS(omega t)
			 2    2	   2	      3/2
		       (d  - r  SIN (omega t))
(C4) ratsimp(%);

	       2  4    4		  2    2    2
(D4) - (- omega  r  SIN (omega t) + SQRT(d  - r  SIN (omega t))

       2  3		    2		  2	 2
 (omega  r  COS(omega t) SIN (omega t) - d  omega  r COS(omega t))

    2	   2  2	   2		 2      2  2    2
 + d  omega  r  SIN (omega t) - d  omega  r  COS (omega t))

	2    2	  2	        2    2		   2
/(SQRT(d  - r  SIN (omega t)) (r  SIN (omega t) - d ))
(C5) tex(%);

$$-{{-omega^{2}\>r^{4}\>\sin ^{4}\left(omega\>t\right)+\sqrt{d^{2}-r
 ^{2}\>\sin ^{2}\left(omega\>t\right)}\>\left(omega^{2}\>r^{3}\>
 \left(\cos omega\>t\right)\>\sin ^{2}\left(omega\>t\right)-d^{2}\>
 omega^{2}\>r\>\left(\cos omega\>t\right)\right)+d^{2}\>omega^{2}\>r
 ^{2}\>\sin ^{2}\left(omega\>t\right)-d^{2}\>omega^{2}\>r^{2}\>\cos 
 ^{2}\left(omega\>t\right)}\over{\sqrt{d^{2}-r^{2}\>\sin ^{2}\left(
 omega\>t\right)}\>\left(r^{2}\>\sin ^{2}\left(omega\>t\right)-d^{2}
 \right)}}$$
(D5) 				     FALSE
(C6)