Kinematic differential geometry of a rigid body in spatial motion using dual vector calculus: Part-I

摘要

In the present paper, the geometrical properties of a line trajectory in spatial motion are researched by using dual vector calculus. The invariants of a line trajectory generated by spatial motion are represented by that of the dual curve on the dual unit fixed sphere. Meanwhile the dual curvature theories or the dual geodetic Euler–Savary analogue is set up.Some special cases of curvatures of a dual curve on the dual unit fixed sphere leads to the sets of lines with special kinematic meanings in the moving space.These lines will be discussed in the consecutive paper.