This results in the creation of isochrones, showing the set of possible positions of the boat at a given time, which are a useful tool for the navigator.
12.
One way the curve can be an isochrone is if the Lagrangian is that of a simple harmonic oscillator : the height of the curve must be proportional to the arclength squared.
13.
Isochrone maps can be used to show the time taken for runoff water within a drainage basin to reach a lake, reservoir or outlet, assuming constant and uniform effective rainfall.
14.
In various application areas, isocontours have received specific names, which indicate often the nature of the values of the considered function, such as isochrone, isoquant and indifference curve.
15.
A tautochrone or isochrone curve is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point.
16.
In May 1690 in a paper published in " Acta Eruditorum ", Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation.
17.
The isochrone, or curve of constant descent, is the curve along which a particle will descend under gravity from any point to the bottom in exactly the same time, no matter what the starting point.
18.
"' Mapumental "'is free and open source software by mySociety for displaying journeys in terms of how long they take, rather than by distance, a technique also known as isochrone or geospatial mapping.
19.
An additional defining property of the semicubical parabola is that it is an "'isochrone curve "', meaning that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods.
20.
If the initial mass function of the open cluster is known, isochrones can be calculated at any age by taking every star in the initial population, using numerical simulations to evolve it forwards to the desired age, and plotting the star s luminosity and magnitude on the HR diagram.
