Abstract
In this study, sliding velocity, pole lines, hodograph, and acceleration poles of two-parameter Lorentzian homothetic motions at positions are obtained. By defining two-parameter Lorentzian homothetic motion along a curve in Lorentzian space , the theorems related to this motion and characterizations of the trajectory surface are given. MSC:53A17, 53B30, 14H50.
Highlights
To investigate the geometry of the motion of a line or a point in the motion of space is important in the study of space kinematics or spatial mechanisms or in physics
Firstly we introduce two-parameter homothetic motions in a Lorentzian plane L and we calculate the pole points obtained from Lorentzian homothetic motion
5 Parametrizations of trajectory surfaces we find some parametrizations of the trajectory surfaces obtained from two-parameter motions in a Lorentzian space
Summary
To investigate the geometry of the motion of a line or a point in the motion of space is important in the study of space kinematics or spatial mechanisms or in physics. The pole points of Lorentzian homothetic motions MI obtained from Lorentzian homothetic motions MII on a moving plane at the position of (λ, μ) = ( , ) give the following results. The equation of the pole points of Lorentzian homothetic motions MI obtained from Lorentzian homothetic motions MII on a fixed plane is (haθ ̇ – hb ̇)xp – (hbθ – ha ̇)yp = a(haθ – hb ̇) – b(hbθ – ha ̇), at the position of λ = μ = and when |h | = |hθ|. The pole points of Lorentzian homothetic motions MI obtained from Lorentzian homothetic motions MII on a fixed plane at the position of (λ, μ) = ( , ) give the following results.
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