Shortest path in 3d with minimum turning radius

I want to calculate shortest trajectory of a rocket between two points
in 3D space. Directions in starting and ending points are given. The
rocket has certain minimum turning radius.

The trajectory has to consist of starting arc, straight line, and
ending arc. The line is tangent for both arcs. The first arc contains
the starting point and its tangent there is equal to the starting
direction. The second arc has similar properties for the ending point
and ending direction.

When I tried to solve this problem I obtained a system of quadratic
equations hard to solve. Therefore, I am looking for some relevant
resources. Do you have any suggestions?

Mirek.