How to find the orthogonal trajectories - Krista King Math
2019年1月20日 · In the example below we’ll show how to use calculus to find the orthogonal trajectories, but for now we’ll give away the answer so that we can sketch the family of orthogonal trajectories and see that they are perpendicular to the original family.
Orthogonal trajectory - Wikipedia
In mathematics, an orthogonal trajectory is a curve which intersects any curve of a given pencil of (planar) curves orthogonally. For example, the orthogonal trajectories of a pencil of concentric circles are the lines through their common center (see diagram).
Orthogonal Trajectory – Definition and Examples - The Story of ...
2023年6月30日 · In the realm of mathematics, an orthogonal trajectory refers to a family of curves that intersect another family of curves at right angles (90 degrees), hence the term “orthogonal,” which is derived from the Greek words for “right” (ortho) and “angle” (gonia).
Orthogonal Trajectories - math24.net
The common approach for determining orthogonal trajectories is based on solving the partial differential equation: \[\nabla f\left( {x,y} \right) \cdot \nabla g\left( {x,y} \right) = 0,\] where the symbol \(\nabla\) means the gradient of the function \(f\left( {x,y} \right)\) or \(g\left( {x,y} \right)\) and the dot means the dot product of the ...
A curve that intersects each member of a given family of curves at right angles (orthog-onally) is called an orthogonal trajectory of the family. Each line in (c) is an orthogonal trajectory of the family of circles (a) [and conversely, each circle in (a) is …
Orthogonal Trajectories - Differential Equation | Definition
Learn the definition and examples of orthogonal trajectories in differential equations with this educational YouTube video.
MATHEMATICA TUTORIAL, Part 1.2: Orthogonal Trajectories
2024年11月27日 · Two curves are orthogonal or perpendicular at a point if their respective tangent lines to the curves at that point are perpendicular. The word orthogonal comes from the Greek ορθη (right) and γωνια (angle); the word trajectory …
Orthogonal Trajectory: A General Guide - Unacademy
A curve that crosses any curve of a given pencil of (planar) curves orthogonally is called an orthogonal trajectory in mathematics. For example, the lines through the common center of a pencil of concentric circles are orthogonal trajectories (see diagram).
Orthogonal trajectory | Linear Motion, Vector Calculus
Orthogonal trajectory, family of curves that intersect another family of curves at right angles (orthogonal; see figure). Such families of mutually orthogonal curves occur in such branches of physics as electrostatics, in which the lines of force and …
4.5: Applications to Curves - Mathematics LibreTexts
Orthogonal Trajectories. Two curves C1 and C2 are said to be orthogonal at a point of intersection (x0, y0) if they have perpendicular tangents at (x0, y0). (Figure 4.5.10 ). A curve is said to be an orthogonal trajectory of a given family of curves if it is orthogonal to every curve in the family.
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