An infinitisemally small ball is placed at the top of a ramp which has a height of 1m and ends 1m away horizontally. What is the optimal curve of the ramp to minimize time taken for the ball to reach the base? I've tried a spreadsheet simulation of quadratic, cubic, circular and cycloidal functions; and the best so far seems to be the cycloid. Is this true; can it be proven? Thanks
2026-04-03 08:26:16.1775204776
What curved ramp transports a ball from (1,1) to (0,0) most quickly, under the acceleration of gravity, with no friction or air resistance?
141 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MATHEMATICAL-PHYSICS
- Why boundary conditions in Sturm-Liouville problem are homogeneous?
- What is the value of alternating series which I mention below
- Are there special advantages in this representation of sl2?
- Intuition behind quaternion multiplication with zero scalar
- Return probability random walk
- "Good" Linear Combinations of a Perturbed Wave Function
- Yang–Mills theory and mass gap
- Self adjoint operators on incomplete spaces
- Algebraic geometry and algebraic topology used in string theory
- Compute time required to travel given distance with constant acceleration and known initial speed
Related Questions in CALCULUS-OF-VARIATIONS
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Weak formulation of Robin boundary condition problem
- Why is the index of a harmonic map finite?
- Variational Formulation - inhomogeneous Neumann boundary
- Relationship between Training Neural Networks and Calculus of Variations
- How to prove a Minimal Surface minimizes Surface Tension
- Derive the Euler–Lagrange equation for a functional a single variable with higher derivatives.
- Does the covariant derivative commute with the variational derivative?
- Derivative of a functional w.r.t. a single point?
- calculus of variations with double integral textbook?
Related Questions in NONLINEAR-OPTIMIZATION
- Prove that Newton's Method is invariant under invertible linear transformations
- set points in 2D interval with optimality condition
- Finding a mixture of 1st and 0'th order Markov models that is closest to an empirical distribution
- Sufficient condition for strict minimality in infinite-dimensional spaces
- Weak convergence under linear operators
- Solving special (simple?) system of polynomial equations (only up to second degree)
- Smallest distance to point where objective function value meets a given threshold
- KKT Condition and Global Optimal
- What is the purpose of an oracle in optimization?
- Prove that any Nonlinear program can be written in the form...
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?