Cartesian Coordinates

Some articles on cartesian coordinates, coordinate, coordinates, cartesian:

Orthogonal Curvilinear Coordinates in 3d - Coordinates, Basis, and Vectors
... A point in 3d space can be defined using Cartesian coordinates (x, y, z), or in another system (q1, q2, q3), as shown in Fig ... The latter is a curvilinear coordinate system ... The quantities (q1, q2, q3 ) are the curvilinear coordinates of a point P ...
Computing The Area of A Triangle - Using Line Integrals
... While the line integral method has in common with other coordinate-based methods the arbitrary choice of a coordinate system, unlike the others it makes no arbitrary choice of vertex of ... Furthermore the choice of coordinate system defined by L commits to only two degrees of freedom rather than the usual three, since the weight is a local distance (e.g ... When working in polar coordinates it is not necessary to convert to cartesian coordinates to use line integration, since the line integral between consecutive vertices (ri,θi ...
Mechanics Of Planar Particle Motion - Fictitious Forces in A Local Coordinate System
... See also Generalized forces, Curvilinear coordinates, Generalized coordinates, and Frenet-Serret formulas In discussion of a particle moving in a circular orbit ... By using a coordinate system commonly used in planar motion, the so-called local coordinate system, as shown in Figure 1, it becomes easy to identify formulas for the centripetal inward force normal to ... To introduce the unit vectors of the local coordinate system shown in Figure 1, one approach is to begin in Cartesian coordinates in an inertial framework and ...
Mechanics Of Planar Particle Motion - Fictitious Forces in Curvilinear Coordinates
... See also Curvilinear coordinate system and Covariant derivative To quote Bullo and Lewis "Only in exceptional circumstances can the configuration of Lagrangian system be described by a vector in ... as a differentiable manifold." Instead of Cartesian coordinates, when equations of motion are expressed in a curvilinear coordinate system, Christoffel symbols appear in the ... frame of reference in curvilinear coordinates ...
Conic Section - Cartesian Coordinates - Modified Form
... for a general conic section is then given in the polar form by and in the Cartesian form by From the above equation, the linear eccentricity (c) is given by ...