Tagged Questions

The process of determining the best solution among all possible solutions given a set of constraints.

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What is the best path for a given initial and final state?

I am trying to calculate an efficient acceleration curve given starting and final positions and velocities. I'm assuming no friction, and that the acceleration can be applied in any direction at any ...
589 views

Is there a closed form solution to the Esdale river problem?

This is probably not well known problem but it looks like open problem. What kind of methods there are to find a closed form solution to the physical situation? Can you solve this problem? You're ...
720 views

How does the shape (form; not cross-section) of a spring impact performance?

Cylindrical compression springs are everywhere and then some applications choose other forms like rectangular or unique polygonal form. What impact does the form of a compression spring have and how ...
148 views

What are circles on broth (eating soup) surface?

Think about broth in the soup, usually it has circles on its surface. What are their properties? Why there are many of them (not a few big blobs)? Are they depended on liquid's temperature? What needs ...
226 views

Optimization of Bottle Rocket Water Level

My (entry-level) physics class is building bottle rockets, and we are competing to build the longest-flying bottle rocket. The rockets are filled partway (we get to decide how much to fill them) with ...
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Optimal curve for a marble drop [closed]

I'm doing a marble roller coaster project for my physics class at school. The first part of our roller coaster involves a marble falling downwards into a curve that will drop then go up 12 inches. ...
1k views

What are the optimal shapes, if any, for fractal antennae?

A DIY fractal antenna project is described at http://www.htpc-diy.com/2012/04/diy-flexible-fractal-window-hdtv.html Mainly idle curiosity, but I was wondering what the principles behind these might ...
1k views

Utilizing maximum acceleration $a$ for displacement $d$ with initial velocity $v_0$ and final velocity $v_1$

Problem My goal is to move an object from point a to b (displacement $d$) as fast as possible utilizing the maximum available acceleration $a_{max}$, taking into account the initial velocity $v_0$ ...
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Can you help me solve this using the current value Hamiltonian? [closed]

Okay, so I am getting a little stuck on this question, I will post it and then tell you how far I get. $$max - \int_0^2 (x^2 + u^2)e^{-0.03t}dt\,$$ $$x' = x-2u$$ $$x(0) = 3$$ $$x(2)free$$ ...
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What is the path taken by a “cable car”?

A well known result in variational calculus & Lagrangian Mechanics is the solution to the "brachistochrone" problem, where it is found the path connecting two points, A & B such that the time ...
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Optimization of transfer matrix method for quarter wave stack

Does anyone have any tips for Matlab optimization algorithms to use with a 2x2 Transfer Matrix Method Program? I have written a Matlab function that takes a series of refractive index values and ...
100 views

Pareto efficiency and Standard Model parameters

Pareto Efficiency is a well understood concept in economics, which basically is a condition where no one actor could be made better off without some one being made worse off. This condition allows ...
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Dual methods in structure optimization

I am studying Structure Optimization, and the teacher took a few weeks to detail dual methods, but I don't get why it is useful. From an optimization problem with n...
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what's the world record in finding the ground state of the 3D Ising model

Finding the ground state of the 3D ising model (with no magnetization) is known to be NP-complete. Just wondering what is the biggest size cubic lattice someone has found the ground state of for this ...
111 views

Maximize time of flight and range at the same time in projectile motion

Given the equations of projectile motion (no air resistance), it is easy to find the launching angle theta that produces the maximum range. That angle is 45 degrees. The maximum time of flight is ...
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Using differentials to optimize a function [closed]

I've read in a paper by Tevian Dray an alternative way to solve optimization problems manipulating "differentials". Here is an example of how it works (next I quote the paper). Consider the ...
210 views

Is it possible to work out the shortest time in which a body can travel a certain distance if all that is provided is the max a, max -a, v1, v2 and s?

Is it possible to calculate the shortest time it takes a body to travel a certain distance if the only information provided is its maximum acceleration, its maximum retardation and the distance it ...
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Searching for acceleration to minimalize path or time

I am thinking about motion of one point starting from $(0,0)$ and with velocity $\mathbf{v}(0)$. What is the acceleration $\mathbf{a}(t)$ with condition $|\mathbf{a}(t)|<M$ that minimalize path/...
I'm looking for an equation to find the time it will take for a position displacement to happen, given known $V_{max}$, a (known) constant acceleration, deceleration, jerk, and displacement... and an ...