The process of determining the best solution among all possible solutions given a set of constraints.
Questions tagged [optimization]
95 questions
17
votes
1 answer
Non-uniform Circular motion velocity optimization
Consider the following problem:
A vehicle (modeled as a particle) enters into a circular arc trajectory at point $s_1$ (given), see figure below. If at $s_2$ the speed of the vehicle is not to exceed a given speed $v_2 \geq 0$, find $v(s)$ (a…
bitpancakes
- 191
16
votes
5 answers
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 time.
Given:
$p_0$ = starting position
$v_0$ =…
generesque
- 163
9
votes
5 answers
Maximal Gravity
I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin:
Given a point $P$ in space, and given a piece of malleable material of constant density, how should you shape and place the material…
Bernhard Heijstek
- 1,997
8
votes
5 answers
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 slower in order to avoid the extremes to overcome the…
DarioP
- 5,205
7
votes
3 answers
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 do you calculate an optimal solution?
user1066701
- 89
- 1
- 5
6
votes
4 answers
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 passively flowing downstream in the middle of a…
curious
- 99
5
votes
1 answer
Could two concatenated cycloids be an optimal solution to the Brachistochrone problem?
The following is a specific instance of the brachistochrone
problem, which I first encountered in grad school, and I
have occasionally used as hw problem in teaching CM.
A particle is started from rest at the origin and constrained to fall under…
Thomas
- 19,250
5
votes
3 answers
Control systems from a physicist's perspective
I am highly interested in the study of control systems theory. However it seems that almost all books are written by electronics or mechanical engineers.
Due to this they generally omit many things. For instance every single textbook in controls…
5
votes
2 answers
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 complicate matters), then we can compute the…
JCooper
- 385
5
votes
1 answer
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 water, placed on the launcher, and filled with…
5
votes
2 answers
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 $(v'_x, y'_x)$. What path takes the smallest…
Matthew Piziak
- 335
5
votes
1 answer
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 to be added to water so these kind of circles…
ile
- 153
4
votes
2 answers
How to solve self-consistent equations numerically?
I am working in condensed matter, where I'm required to solve an integral self consistently which is of the form,
$$
\Delta = \int f(x,y,\Delta,\mu,h)dxdy
$$
Basically I need to find value of $\mu,\,\Delta$ such that the above equation is satisfied…
user235410
- 51
4
votes
1 answer
Given a 2D path and maximum acceleration, what is the minimum time to reach the end?
As stated in the title, I want to find an expression or a way to calculate the minimum time to go from one point of a path to another when the path is given and acceleration is restricted.
Thus far, I have tried to consider a simplified situation…
110112345
- 141
4
votes
2 answers
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 temperature:
$$P(\{S\}) \sim e^{-E(\{S\})/kT}$$
(where…
Alex319
- 209