
	Molecular Dynamics Simulations

As opposed to collisions between atoms  or  molecules  collisions
between the grains of sand are ``inelastic'' which means that en-
ergy is lost. In fact, all the collisions we encounter  in  daily
life (between cars, billiard balls or people) are inelastic since
always some energy will be transformed into heat. Let us consider
for instance tennis balls, called ``particles'' in the following,
as a rather good (although a little simplified) representation of
sand  grains  and  let  us try to calculate on the computer their
trajectories and collisions by ``Molecular Dynamics''.

Molecular Dynamics  is  a  direct  calculation  of  the  position
x(t+dt)  of  the particles at time t+dt knowing the position x(t)
of the particles at time t. First we  calculate  all  the  forces
that  act  at time t which besides gravity are all the forces due
to collisions either with walls or with other particles.   Divid-
ing the sum of all the forces that act on a given particle by its
mass gives the accelation a(t) (Newton's law).  From that we cal-
culate the velocity v(t+dt) at time t+dt by adding a(t)*dt to the
velocity v(t) at time t  and  the  positions  x(t+dt)  by  adding
v(t)*dt to x(t).

Which are the forces that act? On one hand one always has  gravi-
ty.  On earth the acceleration due to gravity is 9.8 m/sec but it
could be fun to watch how things would behave on the moon  or  on
Jupiter  and  for  that reason we will always leave the option to
change the accelation g of the gravity.   All  other  forces  act
when  particles  collide  either  with  other particles or with a
wall.
/*
	GettingStarted;
	Forces;
	Hopper;
	Vibration;
	Billiard;
