2009

time t2 we find the ball in the middle of the windy region. This region causes
a large wind force to act on the ball which is taken into account during the
next time step. At that point we reevaluate the math and determine a new
position for the ball at time t3. This is different from the position determined
in the simulation on the left, even though the same amount of time has been
simulated in each case. In other words, the wind has blown the ball to the
left a bit and has reduced the velocity of the ball
In general, the smaller the time step taken, the more accurate the result at the
end of the time step. Thus, to step forward in time by a large time step t it is
better to split this into n steps of a smaller time interval t/n.
This is also true of the math. As the simulation becomes more complex, the
math required to calculate the new positions and velocities of objects in a
simulation also becomes more complex, and as a result the guesses produced
by the math give progressively less-accurate results.
So the principle is to take small time steps, evaluate all the forces acting on
the objects, determine the new positions and velocities (and other parameters)
of the objects at the end of the time steps, and then start over. We end up
with a series of snapshots of the state of the system as it evolves, as shown in
the following illustration.
Introducing Dynamics Simulation | 3893