I want to structure the second-order dynamical systems in the form of first-order representation. There are several first-order representations that exist, which is the most appropriate one?
This is can be done using chain rule, substitution along with y'=w, which will reduce a Type 2 equation to first order equation for w. Once w is determined, then integrate to find y.
Dear Garba Shu'iabu this is a system not a single equation. I want to make the representation, not to find the solution.
Thanks.
For instance, you can structure x''=ax'+bx+c being a second order differential equation to system of linear equations as follows:
Let x=x_1
x'=(x_1)'=x_2
x''=(x_1)''=(x_2)'
Thus, the system of first order differential equation is given by:
(x_1)'=x_2
(x_2)'=-ax_2-bx_1-c
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix