Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: The results show that the calculation of quintic polynomial trajectory planning algorithm is relatively heavy, and it can ensure the continuity of angular acceleration and stable operation of motor.
Abstract: In order to solve the problem of joint acceleration mutation in the cubic polynomial trajectory planning algorithm, the algorithm of the quintic polynomial trajectory planning is studied. The results show that the calculation of quintic polynomial trajectory planning algorithm is relatively heavy, and it can ensure the continuity of angular acceleration and stable operation of motor. Trajectory planning is carried out in Cartesian space by using the spatial line and the spatial arc interpolation algorithm. MATLAB robotics toolbox is used to model the motion system and simulate the motion, which verifies the correctness and feasibility of the linear interpolation and circular interpolation algorithm.
5 citations
TL;DR: The unconditional stability and convergence in maximum norm with order O(τ2+h4)$O({\tau }^{2}+h^{4})$ are proved by using the energy method.
Abstract: A compact finite difference (CFD) scheme is presented for the nonlinear Schrodinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order $O({\tau }^{2}+h^{4})$
are proved by using the energy method. A numerical experiment is presented to support our theoretical results.
5 citations
TL;DR: In this article , the conservation laws for optical solitons with cubic-quantic-septic-nonic nonlinearity were presented and the adiabatic dynamics of the conserved quantities were obtained by the usage of soliton perturbation theory.
5 citations
Patent•
21 Sep 2011
TL;DR: In this article, a method for designing a roll shape of a variable-crown working roll which is used for plate shape control in strip steel production and has quartic crown control capacity is presented.
Abstract: The invention provides a method for designing a roll shape of a variable-crown working roll which is used for plate shape control in strip steel production and has quartic crown control capacity. By using the method, the approximate linear relationship between a no-load roll gap quadratic crown and the channeling shift amount of a roll is ensured, and simultaneously the quadratic crown capacity of wide and narrow strip steel can be balanced. By utilizing the corresponding relationships among roll shape coefficients provided by the invention, a variable-crown roll shape of a quintic polynomialfunction can be designed flexibly according to the requirement on quadratic and quartic crown control. The method has the characteristics that: the roll shape designed by the method can change the characteristic that a quadratic crown control range is in square drop along with the reduction of the width of the strip steel. Compared with a cubic CVC roll shape, the roll shaped designed by the method can not only provide the quartic crown control capacity, but also provide higher quadratic crown control capacity. Compared with a quintic CVC roll shape designed by other methods, the method has convenient design, can design flexibly according to the requirement on the quartic crown control, and can balance the quadratic crown control capacity of the wide strip steel and the narrow strip steel.
5 citations
TL;DR: In this article , the generalized space-time fractional cubic-quintic nonlinear Schrödinger (FCQNLS) equation was considered in the presence of complexified parity reflection-time reversal (PT)−symmetric Scarff-II potential.
5 citations