ASL STEM

Brachistochrone Problem Sign Video

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Definition

One of the famous problems in the history of mathematics is the brachistochrone problem: to find the curve along which a particle will slide without friction in the minimum time from one given point P to another Q, the second point being lower than the first but not directly beneath it. The word "brachistochrone" comes from the Greek words brachistos, meaning shortest, and chronos, meaning time.

Source: Elementary Differential Equations and Boundary Value Problems - William Boyce & Richard DiPrima

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> Mathematics

> Differential Equations

> Brachistochrone Problem

+ Critical Point

+ Direction Fields *

+ Initial Value Problem *

+ Initial Condition *

+ Integrating Factor *

+ Equilibrium Solution *

+ Rate Function *

+ General Solution *

+ Integral Curve *

+ Ordinary Differential Equation *

+ Partial Differential Equation *

+ Linearization *

+ First Order Linear Equation *

+ Phase Plane *

+ Environmental Carrying Capacity *

+ Semistable Equilibrium Solution *

+ Bifurcation Point *

+ Euler Method *

+ Difference Differential Equation *

+ Singular Point *

+ Nonhomogeneous *

+ Principle Of Superposition *

+ Wronskian Determinant *

+ Fundamental Set Of Solutions *

+ Variation Of Paramters *

+ Quasi Period *

+ Amplitude Modulation *

+ Quasi Frequency *

+ Euler Equation *

+ Regular Singular Point *

+ Irregular Singular Point *

+ Hermite Equation *

+ Chebyshev Equation *

+ Ordinary Point *

+ Legendre Equation *

+ Indicial Equation *

+ Bessel's Equation *

+ Laplace Transform *

+ Heaviside Step Function *

+ Unit Step Function *

+ Delta Function *

+ Transfer Function *

+ Simple Eigenvalue *

+ Phase Portrait *

+ Fixed Point Node *

+ Stable Node *

+ Unstable Node *

+ Improper Node *

+ Spiral Point *

+ Similarity Transformation *

+ Heun's Method *

+ Predictor Corrector Method *

+ Spiral Source *

+ Spiral Sink *

+ Basin Of Attraction *

+ Orbital Stability *

+ Strange Attractor *

+ Fourier Sine Series *

+ Heat Conduction Equation *

+ Thermal Diffusivity *

+ Boundary Conditions *

+ Two Point Boundary Value Problem *

+ Eigenfunctions *

+ Mutually Orthogonal *

+ Fourier Cosine Series *

+ Wave Equation *

+ Natural Frequency *

+ Natural Mode *

+ Laplace's Equation *

+ Potential Equation *

+ Dirichlet Problem *

+ Neumann Problem *

+ Lagrange's Identity *

+ Sturm Liouville Equation *

+ Continuous Spectrum *

+ Collocation Method *

+ Mean Squared Error *

- Brachistochrone Problem *

+ Lyapunov Function *

* video needed

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