orthogonal coordinates वाक्य
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- Other differential operators such as \ nabla \ cdot \ mathbf { F } and \ nabla \ times \ mathbf { F } can be expressed in the coordinates ( \ mu, \ nu, \ varphi ) by substituting the scale factors into the general formulae found in orthogonal coordinates.
- If, say, we wanted to find integrals in non-orthogonal coordinate systems, would triangles be better ( Like, if instead of the x and y axes being perpendicular, if they made a 45?angle ) ?-- ?06 : 12, 5 April 2007 ( UTC)
- Expressing the Navier Stokes vector equation in Cartesian coordinates is quite straightforward and not much influenced by the number of dimensions of the euclidean space employed, and this is the case also for the first-order terms ( like the variation and convection ones ) also in non-cartesian orthogonal coordinate systems.
- Other differential operators such as \ nabla \ cdot \ mathbf { F } and \ nabla \ times \ mathbf { F } can be expressed in the coordinates ( " ? ", " ? " ) by substituting the scale factors into the general formulae found in orthogonal coordinates.
- In many applications of computational geometry, when a problem is stated for a set of rectilinear polygons, it is very often implicitly assumed that these polygons have the same alignment ( in fact, aligned to the same orthogonal coordinate axes ), and hence the term " isothetic polygons " would be less ambiguous.
- While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum mechanics, fluid flow, electrodynamics and the diffusion of chemical species or heat.
- For orthogonal coordinates and Hamiltonians that have no time dependence and are quadratic in the generalized momenta, " S " will be completely separable if the potential energy is additively separable in each coordinate, where the potential energy term for each coordinate is multiplied by the coordinate-dependent factor in the corresponding momentum term of the Hamiltonian ( the "'Staeckel conditions "').
- "' Lode coordinates "'( z, r, \ theta ) or "'Haigh-Westergaard coordinates "'( \ xi, \ rho, \ theta ) . are a set of orthogonal coordinate system is named in honor of the German scientist Dr . Walter Lode because of his seminal paper written in 1926 describing the effect of the middle principal stress on metal plasticity.
- I'm studying permutations and combinatorics for this entrance exam and i just thought of a really interesting ( not sure if its feasible ) problem : In a 3d orthogonal coordinate system, in how many ways could u move from a point ( 2, 3, 5 ) to a point ( 9, 11, 14 ) [ ( or in general from ( x, y, z ) to ( x', y', z') ] assuming that u could only move parallel to the coordinate axes and on integral points . Is there some sort of generalized algorithm to find the solution ? ? 59.183.42.170 18 : 24, 6 March 2007 ( UTC)
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