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In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. [1] "
Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations.It provides many useful specialized functions and equations for the solution of thermodynamics and heat transfer problems, making it a useful and widely used program for mechanical engineers working in these fields.
The equation of a line is given by = +. The equation of the normal of that line which passes through the point P is given y = x 0 − x m + y 0 {\displaystyle y={\frac {x_{0}-x}{m}}+y_{0}} . The point at which these two lines intersect is the closest point on the original line to the point P.
If a planar curve in is defined by the equation = (), where is continuously differentiable, then it is simply a special case of a parametric equation where = and = (). The Euclidean distance of each infinitesimal segment of the arc can be given by:
A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters :. Parametric representation is a very general way to specify a surface, as well as implicit representation .
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
The Fermat spiral with polar equation = can be converted to the Cartesian coordinates (x, y) by using the standard conversion formulas x = r cos φ and y = r sin φ.Using the polar equation for the spiral to eliminate r from these conversions produces parametric equations for one branch of the curve: