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

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Number of blades in a helicopter rotor

I was wondering how it is possible to determine what is the optimal number of blades in a helicopter rotor. I think that the length of the blade is involved as a longer blades would have to spin ...
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0answers
23 views

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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2answers
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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0answers
54 views

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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2answers
105 views

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. ...
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1answer
42 views

Optimizing the second, third,… eigenvalues - applications

I'm working on some topics related to spectral optimization as a function of the domain. For example it is known for almost a century (lord Rayleigh and Faber, Krahn) that the shape which minimizes ...
5
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1answer
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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5answers
713 views

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 ...
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0answers
58 views

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 ...
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1answer
100 views

Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
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1answer
82 views

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 ...
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0answers
47 views

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/...
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2answers
153 views

How long does it take to optimally change position and velocity?

A spaceship moving in two dimensions is at position $(x, y)$ and has a velocity $(v_x, v_y)$. It also has a maximum acceleration $a_{max}$. Its goal is to be at position $(x', y')$ with a velocity of $...
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1answer
253 views

Physics problems requiring optimization? [closed]

I would like to know if there are simple benchmark physics problems to test a Genetic Algorithm C++ library I developed. The library supports single and multi-objective constrained optimization and I ...
2
votes
0answers
39 views

Coefficients and Parameters for contracted Gaussian basis sets

This is a repost from Chemistry.stackexchange in the hopes that someone here will be able to help me. Any help at all would be greatly appreciated. As far as I understand, an STO-NG contracted ...
2
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0answers
117 views

Particle Collision with Static System

I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is : The method by which I can reduce the number of ...
2
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1answer
64 views

Converting Point Gradients to Rotational Representation

I'm a PhD student in an unrelated field. It's been a very long time since I've done physics, and I've run into a problem in my research which I think is actually a physics problem. Basically, I have ...
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0answers
79 views

Optimal Airplane trajectory

The last time I took a plane the following problem crossed my mind. Setting: take the Earth and neglect its rotation around the Sun. It then only rotates on itself with angular velocity $\Omega$. ...
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1answer
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 ...
5
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1answer
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 ...
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1answer
103 views

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 ...
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4answers
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 ...
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2answers
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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1answer
4k views

Help finding Delta T for a known position displacement with known accel/decel, etc

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 ...
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1answer
193 views

What lifting mechanism is likely to have the best energy recovery ratio? [closed]

Suppose I was designing an apparatus which needed to lift 250kg 5cm high, hold it there for a few seconds, and then lower the object back to the original height. Such a process would need to be ...
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2answers
112 views

Determining the probability of a particular site having a particular spin in an Ising model

Given an Ising model, we have the energy formula: $E= - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j$ and we have the probability of a given state, given the energy of that state and the ...
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2answers
636 views

The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available

If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
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0answers
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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0answers
33 views

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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3answers
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 ...
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1answer
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 ...
2
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1answer
142 views

Good algorithm for in-experiment 1-D optimization?

I'm running an experiment -- for the question, it doesn't matter which one, but I'm measuring an optical intensity $I$ as a function of two parameters: reflection angle $\theta$ and wavelength $\...