Jacobi Elliptic Functions As Solutions of Nonlinear Ordinary Differential Equations
The derivatives of the three basic Jacobi elliptic functions are:
With the addition theorems above and for a given k with 0 < k < 1 they therefore are solutions to the following nonlinear ordinary differential equations:
- solves the differential equations
-
- and
- solves the differential equations
-
- and
- solves the differential equations
-
- and
Read more about this topic: Jacobi Elliptic Functions
Famous quotes containing the words jacobi, functions, solutions, ordinary and/or differential:
“During the long ages of class rule, which are just beginning to cease, only one form of sovereignty has been assigned to all menthat, namely, over all women. Upon these feeble and inferior companions all men were permitted to avenge the indignities they suffered from so many men to whom they were forced to submit.”
—Mary Putnam Jacobi (18421906)
“If photography is allowed to stand in for art in some of its functions it will soon supplant or corrupt it completely thanks to the natural support it will find in the stupidity of the multitude. It must return to its real task, which is to be the servant of the sciences and the arts, but the very humble servant, like printing and shorthand which have neither created nor supplanted literature.”
—Charles Baudelaire (18211867)
“Football strategy does not originate in a scrimmage: it is useless to expect solutions in a political compaign.”
—Walter Lippmann (18891974)
“Youth demands more than ordinary life. Age clings to it.”
—Mason Cooley (b. 1927)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (18961948)