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- Orthogonal_trajectory abstract "In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles. The problem is classical, but is now understood by means of complex analysis; see for example harmonic conjugate.For a family of level curves described by , where is a constant, the orthogonal trajectories may be found as the level curves of a new function by solving the partial differential equationfor . This is literally a statement that the gradients of the functions (which are perpendicular to the curves) are orthogonal. Note that if and are functions of three variables instead of two, the equation above will be nonlinear and will specify orthogonal surfaces.The partial differential equation may be avoided by instead equating the tangent of a parametric curve with the gradient of which will result in two possibly coupled ordinary differential equations, whose solutions are the orthogonal trajectories. Note that with this formula, if is a function of three variables its level sets are surfaces, and the family of curves are orthogonal to the surfaces.".
- Orthogonal_trajectory wikiPageExternalLink OrthTraj.html.
- Orthogonal_trajectory wikiPageID "2564849".
- Orthogonal_trajectory wikiPageRevisionID "544109378".
- Orthogonal_trajectory hasPhotoCollection Orthogonal_trajectory.
- Orthogonal_trajectory subject Category:Complex_analysis.
- Orthogonal_trajectory subject Category:Curves.
- Orthogonal_trajectory type Abstraction100002137.
- Orthogonal_trajectory type Attribute100024264.
- Orthogonal_trajectory type Curve113867641.
- Orthogonal_trajectory type Curves.
- Orthogonal_trajectory type Line113863771.
- Orthogonal_trajectory type Shape100027807.
- Orthogonal_trajectory comment "In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles. The problem is classical, but is now understood by means of complex analysis; see for example harmonic conjugate.For a family of level curves described by , where is a constant, the orthogonal trajectories may be found as the level curves of a new function by solving the partial differential equationfor .".
- Orthogonal_trajectory label "Orthogonal trajectory".
- Orthogonal_trajectory label "Orthogonale familie".
- Orthogonal_trajectory label "Trajetória ortogonal".
- Orthogonal_trajectory label "Ортогональные траектории".
- Orthogonal_trajectory sameAs Orthogonale_familie.
- Orthogonal_trajectory sameAs Trajetória_ortogonal.
- Orthogonal_trajectory sameAs m.07nb_l.
- Orthogonal_trajectory sameAs Q2343723.
- Orthogonal_trajectory sameAs Q2343723.
- Orthogonal_trajectory sameAs Orthogonal_trajectory.
- Orthogonal_trajectory wasDerivedFrom Orthogonal_trajectory?oldid=544109378.
- Orthogonal_trajectory isPrimaryTopicOf Orthogonal_trajectory.