Prove that the geodesic between two points A and B on a spherical surface with center O, is found on the curve formed by the intersection of this surface with the plane passing through points A, B and either.I was supposed to use the euler-lagrange equation to show that it is a minimun, so I tried to parameterize the intersection of the plane with a generical sphere but after this process I got stuck. Could anyone help me ?
2026-03-30 00:21:10.1774830070
Prove that the geodesic between two points A and B on a spherical surface is found on the curve formed by the intersection with the plane
106 Views Asked by user63181 https://math.techqa.club/user/user63181/detail AtRelated Questions in MULTIVARIABLE-CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- $\iint_{S} F.\eta dA$ where $F = [3x^2 , y^2 , 0]$ and $S : r(u,v) = [u,v,2u+3v]$
- Proving the differentiability of the following function of two variables
- optimization with strict inequality of variables
- How to find the unit tangent vector of a curve in R^3
- Prove all tangent plane to the cone $x^2+y^2=z^2$ goes through the origin
- Holding intermediate variables constant in partial derivative chain rule
- Find the directional derivative in the point $p$ in the direction $\vec{pp'}$
- Check if $\phi$ is convex
- Define in which points function is continuous
Related Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in GEODESIC
- Length of geodesic line equals distance between two points?
- What's the relation between the Darboux Frame and the Frenet-Serret on a oriented surface?
- Projection from an ellipsoid onto a sphere that preserves geodesy?
- Vector field on a geodesic
- Geodesic lines of the form f(at+b)
- How to actually find a minimizing path on a manifold?
- Calculating the round metric on $S^n$
- Geodesic equation on a codimension 1 submanifold of $\mathbb{R^{n+1}}$
- How can you numerically approximate the geodesic midpoint of 2 points on an ellipsoids?
- Compute geodesic circles on a Surface
Related Questions in EULER-LAGRANGE-EQUATION
- Showing solution to this function by Euler-Lagrange
- Derive the Euler–Lagrange equation for a functional a single variable with higher derivatives.
- Functional with 4th grade characteristic equation
- derivative of double integral in calculus of variation
- When is the Euler-Lagrange equation trivially satisfied?
- Euler-Lagrange and total derivative of partial derivative for function of two variables
- Energy Functional from the Euler-Lagrange Equations
- Find differential equation using variation principle and lagrangian
- Euler-Lagrange equations without lower boundary conditions
- Finding First Variation
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?