Exact Solution of the Nonlinear Differential Equation R(2nd derivative R with respect to t) Plus (3/2)(dR/dt) squared-A(R sup 4) Plus B Equals 0.
Abstract
The nonlinear equation R(2nd derivative R with respect to t) plus (3/2)(dR/dt) squared-A/(R sup4) plus B equals 0 is shown to represent simply periodic motion with a minimum at R sub 1 and a maximum at (R sub 1)(R sub 0) or a maximum at R sub 1 and a minimum at (R sub 1)/(R sub 0). R sub 0 is a function of the ratio A/B and is greater than 1 for A/B>1 and less than 1 for A/B<1. The period of the motion satisfies the simple relation T(1/R sub 0) equals (1/R sub 0)(T(R sub 0)). The exact solution to the above equation is represented in terms of elliptic integrals of the first and second kinds and a simple algebraic function. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 14, 1972
- Accession Number
- AD0740106
Entities
People
- Donald R. Childs
Organizations
- Naval Undersea Warfare Center