Narrow Results

In this paper, differential properties of the one-parameter Lorentzian spatial motions are developed with explicit expressions independent of coordinates systems. In term of this, we calculate the Disteli formulae of a spacelike line trajectory and derive the connections with kinematic geometry of the axodes. Lastly, a theoretical expression of a spacelike inflection line congruence are investigated in detail.

In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space ${𝔻}_1^3$. Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velocity, which are regarded as different forms of Euler–Savary equation form.