File: motion.mac

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/* Computes geodesic equations of motion */

MOTION(DIS):=BLOCK([S],DEPENDS(OMEGA,S),
       FOR I THRU DIM DO
	   EM[I]:IF DIAGMETRIC
		     THEN RATSIMP(DIFF(OMEGA[I],S,2) + 1/2*SUM(
				      DIFF(LG[A,A],OMEGA[I])
				       *DIFF(OMEGA[A],S)^2,A,1,DIM))
		     ELSE RATSIMP(DIFF(OMEGA[I],S,2) 
				+ 1/2*SUM(SUM(DIFF(LG[A,B],OMEGA[I])
				       *DIFF(OMEGA[A],S)*DIFF(OMEGA[B],S),A,
				      1,DIM),B,1,DIM)),
       IF DIS#FALSE THEN FOR I THRU DIM DO LDISPLAY(EM[I]),DONE)$
MOTION2(DIS):=BLOCK([S],DEPENDS(OMEGA,S),
       FOR I THRU DIM DO
	   EMM[I]:DIFF(OMEGA[I],S,2) +			 SUM(SUM(MCS[A,B,I]
				       *DIFF(OMEGA[A],S)*DIFF(OMEGA[B],S),A,
				      1,DIM),B,1,DIM),
       IF DIS#FALSE THEN FOR I THRU DIM DO LDISPLAY(EMM[I]),DONE)$