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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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Journal ArticleDOI
TL;DR: In this article, a wide class of central force field problems are considered within the framework of linear and regular celestial mechanics, and the relations between the coefficients of both functions, in order to arrive to linear equations, are given.
Abstract: Within the framework of linear and regular celestial mechanics, a wide class of central force field problems are considered. We take as potential function a polynomial whose variable is the reciprocal of the distance from the origin, and, as regularizing function the square root of a certain reciprocal polynomial, related to the potential function. The relations between the coefficients of both functions, in order to arrive to linear equations, are given. In particular, the case of a quintic polynomial is analyzed, and an application is made to artificial earth satellites considering harmonicsJ 2,J 3,J 4.

16 citations

01 Jan 2004
TL;DR: In this article, a method for smooth G 2 planar PH quintic spiral transition from straight line to circle is developed, which can be easily applied for practical applications like high way designing, blending in CAD, consumer products such as ping-pong paddles, rounding corners, or designing a smooth path that avoids obstacles.
Abstract: A method for family of G 2 Pythagorean hodograph (PH) quintic spiral transition from straight line to circle is discussed in this paper. This method is then extended to a pair of spirals between two straight lines or two circles. We derive a family of quintic transition spiral curves joining them. Due to exibilit y and wide range of shape control parameters, our method can be easily applied for practical applications like high way designing, blending in CAD, consumer products such as ping-pong paddles, rounding corners, or designing a smooth path that avoids obstacles. 1 Introduction and Description of Method A method for smooth G 2 planar PH quintic spiral transition from straight line to circle is developed. This method is then ex- tended to a pair of spirals transition between two circles or between two non-parallel straight lines. We also develop a method for drawing a constrained guided planar spiral curve that falls within a closed boundary. The boundary is composed of straight line segments and circular arcs. Our constrained curve can easily be controlled by shape control parameter. Any change in this shape control parameter does not eect the continuity and neighbor- hood parts of the curve. There are several problems whose solution requires these types of methods. For example

16 citations

Journal ArticleDOI
TL;DR: In this article, a new quintic discrete nonlinear Schrodinger (QDNLS) equation is studied and exact localized solutions for integrable cases are presented for certain sets of parameters.

16 citations

Journal ArticleDOI
TL;DR: In this paper, two B-spline collocation methods for a class of nonlinear singular Lane-Emden type equations which describe several phenomena in theoretical physics and astrophysics are described.

16 citations

Journal ArticleDOI
23 Jul 2020-Symmetry
TL;DR: The shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries) is discussed and the modeling examples shows that the suggested approach is efficient and easy to implement.
Abstract: Based on quintic trigonometric Bezier like basis functions, the biquintic Bezier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bezier surface but also have exceptional shape adjustment. In order to construct Bezier like curves with shape parameters, we present a class of quintic trigonometric Bezier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surface. In addition to the application of the proposed method, we also discuss the shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries). However, the modeling examples shows that the suggested approach is efficient and easy to implement.

16 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202397
2022254
2021109
2020104
201993
201893