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). Suitable methods for the determination of orthogonal trajectories are provided by solving differential equations. The standard method establishes a first order ordinary differential equation and solves it by separation of variables. Both steps may be difficult or even impossible. In such cases one has to apply numerical methods. Orthogonal trajectories are used in mathematics for example as curved coordinate systems (i.e. elliptic coordinates) or appear in physics as electric fields and their equipotential curves. If the trajectory intersects the given curves by an arbitrary (but fixed) angle, one gets an isogonal trajectory. (Wikipedia).
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Determine if the Vectors are Orthogonal
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determine if the Vectors are Orthogonal
From playlist Calculus
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
In this video, I define the concept of orthogonal projection of a vector on a line (and on more general subspaces), derive a very nice formula for it, and show why orthogonal projections are so useful. You might even see the hugging formula again. Enjoy! This is the second part of the ort
From playlist Orthogonality
Find an Orthogonal Projection of a Vector Onto a Line Given an Orthogonal Basis (R2)
This video explains how t use the orthogonal projection formula given subset with an orthogonal basis. The distance from the vector to the line is also found.
From playlist Orthogonal and Orthonormal Sets of Vectors
11I Orthogonal Projection of a Vector
The Orthogonal Projection of one vector along another.
From playlist Linear Algebra
The geometric view on orthogonal projections
Learning Objectives: 1) Given a vector, compute the orthogonal projection onto another vector This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati
From playlist Linear Algebra (Full Course)
This is the first video of a linear algebra-series on orthogonality. In this video, I define the notion of orthogonal sets, then show that an orthogonal set without the 0 vector is linearly independent, and finally I show that it's easy to calculate the coordinates of a vector in terms of
From playlist Orthogonality
Calculus 9.3 Separable Equations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Calculus II - 6.3.1 Using Separation of Variables to Find General and Particular Solutions
More separation of variables practice, including an application involving Orthogonal Trajectories. Calculus I playlist corresponds to chapters 1-5 of Calculus 11e, Larson, Edwards: https://www.youtube.com/playlist?list=PLl-gb0E4MII1ml6mys-RXoQ0O3GfwBPVM Calculus II playlist corresponds
From playlist Calculus II (Entire Course)
MATH2018 Lecture 3.1 Vector Algebra
A brief review of first year vector algebra and kinematics.
From playlist MATH2018 Engineering Mathematics 2D
ECR Talk: "A tale of two (or more, integrable) billiards", Sean Gasiorek
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Week 2 (MATRIX): ECR Talk by Sean Gasiorek 14 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 Februar
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
DDPS | Trustworthy learning of mechanical systems & Stiefel optimization with applications
In this DDPS talk from June 23, 2022, Georgia Institute of Technology assistant professor Molei Tao discusses data-driven learning and prediction of mechanical dynamics and momentum-accelerated gradient descent algorithms on Riemannian manifolds. Description: The interaction of machine le
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Sarah Post: Rational extensions of superintegrable systems, exceptional polynomials & Painleve eq.s
Abstract: In this talk, I will discuss recent work with Ian Marquette and Lisa Ritter on superintegable extensions of a Smorodinsky Winternitz potential associated with exception orthogonal polynomials (EOPs). EOPs are families of orthogonal polynomials that generalize the classical ones b
From playlist Integrable Systems 9th Workshop
Olivier Le Maître: Global Sensitivity Analysis in Stochastic Systems
Abstract: In this talk we first quickly present a classical and simple model used to describe flow in porous media (based on Darcy's Law). The high heterogeneity of the media and the lack of data are taken into account by the use of random permability fields. We then present some mathemati
From playlist Probability and Statistics
AGACSE2021 Jaroslav Hrdina - GA in control theory
Geometric algebras in mathematics control theory
From playlist AGACSE2021
Topological Constructs and Phases on Polarization Singularities by P. Senthilkumaran
DISCUSSION MEETING STRUCTURED LIGHT AND SPIN-ORBIT PHOTONICS ORGANIZERS: Bimalendu Deb (IACS Kolkata, India), Tarak Nath Dey (IIT Guwahati, India), Subhasish Dutta Gupta (UOH, TIFR Hyderabad, India) and Nirmalya Ghosh (IISER Kolkata, India) DATE: 29 November 2022 to 02 December 2022 VE
From playlist Structured Light and Spin-Orbit Photonics - Edited