Pedal coordinates, solar sail orbits, Dipole drive and other force problems

Pedal coordinates and free double linkage

“…Specifically, certain class of central and Lorentz-like force problems can be easily solved in pedal coordinates algebraically (see Theorem 2). This result was further generalized for a larger set of forces in [8]. In addition, pedal coordinates offer not only a solution but also an understanding.…”

“…Many more dynamical systems and even problems of calculus of variation can be readily translated into pedal coordinates. For detail see [8].…”

“…The purpose of this paper is to showcase these qualities on a non-trivial example that is outside the scope of papers [7,8] -demonstrating that pedal coordinates are far more versatile. Though the example itself is not without interest, the emphasis is laid on the solution's method.…”

On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space

“…The pedal equation of a curve may simplify the calculation of certain properties such as curvature. Several interesting applications of pedal coordinates in many physical phenomena have been demonstrated in recent papers [2–4]. In addition, some other recent papers about the geometry of pedal curves are [5–9].…”

Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane

“…Pedal and contrapedal curves are important mathematical models in classical mechanics, and they have drawn the attention of many scientists. For instance, P. Blaschke showed that the trajectory of a test particle under the influence of central and Lorentzlike forces can be translated into pedal coordinates at once without the need of solving any differential equation (see [1]). P. Blaschke, F. Blaschke and M. Blaschke investigated the orbits of a free double linkage by the technique of pedal coordinates (see [2]).…”