Game Development Reference
In-Depth Information
Figure 6. Fragment of a PlayPhysics game dialogue
orbits of Mars and Jupiter. The station is shaped
like a donut as shown in Figure 8. Athena is rotat-
ing with a constant angular velocity to create an
artificial gravity (g = 9.8 m/s 2 ). The lieutenant,
the student has to navigate Alpha Centauri by
applying Newton's laws of motion for particles
and rigid bodies. In addition, the student has to
know the topics of vectors and linear and circular
kinematics. To make the problem non-trivial, the
values corresponding to Alpha Centauri's initial
location and velocity with respect to Athena
are initialized randomly. A minimum series of
translational and rotational motions have to be
performed to dock with Athena's central part
in the least time possible, since each time that a
motor is ignited to perform a specific motion; α
Centauri's fuel supply is reduced proportionally
to the amount of time that the motor is turned on.
The challenge starts when Alpha Centauri is
launched from Earth on course for the Athena
station. Alpha Centauri has a relative velocity
while approaching Athena, therefore the spaceship
must first stop within a certain distance of Athe-
na's rotational axis by turning on the front engines.
In this part of the challenge, linear motion and
constant deceleration is assumed. Secondly, Alpha
Centauri must align its longitudinal axis with
Athena's rotational axis by applying its upper and
lower engines. Thirdly, Alpha Centauri must match
Athena's rotational velocity by applying its lat-
eral engines. Finally, Alpha Centauri enters into
Athena's docking bay by moving slowly along
its rotational axis.
The exploration variables are the spaceship's
mass and rotational inertia, which are relative to
its longitudinal, zenithal and azimuthal axes. The
longitudinal axis is defined as the axis along the
spaceship length. The zenithal axis is perpendicu-
lar to the spaceship plane and parallel to Athena's
rotation axis. The azimuthal axis is parallel to