/*  
**	The E"otvos Experiment
**		Two objects falling in the gravity field
**		(apparently one of large mass and one of lesser mass)
**		arrive simultaneously if the experiment takes place
**		in a cylinder void of air.
**
**	To solve pose the query:
**		Ma>Mb, two_falling(Ma,Mb,Ta,Tb,D,G).
**
**	Copyright (C) 1995 K J Dryllerakis
**
**	$Id: falling.eu,v 1.3 1995/03/24 15:42:49 kd Exp kd $
*/

two_falling(Ma,Mb,Ta,Tb,D,G):-
	moving_object(Ma,Ta,D,G),
	/* No interaction between objects */
	moving_object(Mb,Tb,D,G).
/* 
**	moving_object(?Mass,?Distance,?GravityConst,?TimeTaken)
*/

moving_object(M,T,D,G):-
	/* Get the force field we are in
	** might also have been supplied as a parameter
	*/
	reals([M,G,T,D,Uf,Ai,Af]),
	formulae([F,S,U,A]),
	gravity_force_field(M,G,F),
	object_kinematics(S,U,A,[0,T],[0,D],[0,Uf],[Ai,Af]),
	object_dynamics(F,M,A).

/*  
**	gravity_force_field(?Mass,?GravityConst,?ForceField)
**		Describe the force field acting on a mass depending
**		on time T(normally one would also include intervals
**		of time -initial to final- so that F would be a function
**		and not just a formula
*/

gravity_force_field(M,G,F):-
	reals([M,G]),
	formula(F),
	F=(M*G)//X.

/*  
**	object_kinematics(?Dist,?Velocity,?Acceleration,?InitialValues)
**		Describes the kinematics of an object
*/

object_kinematics(S,U,A,[Ti,Tf],[Si,Sf],[Ui,Uf],[Ai,Af]):-
	formulae([S,U,A]),
	reals([Si,Sf,Ua,Uf,Ai,Af,Ti,Tf]),
	Ti >=0,
	Tf >=0,
	S=integral(U),
	U=integral(A),
	%continuous(S), /* these will enter when S,U,A are functions */
	%continuous(U),
	S@Ti=Si,S@Tf=Sf,U@Ti=Ui,U@Tf=Uf,A@Ti=Ai, A@Tf=Af.


/*  
**	object_dynamics(?ForceField,?Mass,?Acceleration)
**		Describes Netwon's 2nd law of motion
**		(Simple isn't it?)
*/

object_dynamics(F,M,A):-
	formulae([F,A]),
	real(M),
	(1/M)*F=A.