On decompositions of trigonometric polynomials

Abstract

Let Rt[θ] be the ring generated over R by cos θ and sin θ, and Rt(θ) be its quotient field. In this paper we study the ways in which an element p of Rt[θ] can be decomposed into a composition of functions of the form p = R • q, where R ∈ R(x) and q ∈ Rt(θ). In particular, we describe all possible solutions of the functional equation

Pose overshoot analysis of the marine spherical double plugging in twisting process

“…The following will present the two hydraulic cylinders’ twisting algorithm. 15 The falling distance of inserting hydraulic cylinder is H = L 3 / N . When the first step is performed, the center point C of the sphere moves vertically upwards by the first H , that is…”