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

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