The rocket problem
You are the designer of a rocket which can have only two thrusters each fixed to the main body in anyway you want. You can control these thrusters by pressing 2 separate keys (one for each thruster) in your controller. Assume that you are an expert driver. Can you reach from a pt(0,0,0)to a planet at pt(x', y', z')to pt(x'', y'', z'')to pt(x''',y''',z''') ? Neglect air resistance because there is none.
x, y, z means the x, y, z coordinates of the points
A thruster when on applies a force of constant magnitude in the aligned direction.
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1 solution
The answer is always. This is because the body rocket has its mass and the thrusters will account in rotation of the space ship resulting in free movement in 3d space.