Hi everyone,
I am using a program called AUTO 07p to solve ODE's but having some trouble in a certain part where i have to state the starting solution. I am computing buckling of a straight horizontal beam, using something called the elastica equation. to compute this, i use the following ODE's
θ'' + P/EI * sin θ = 0 (P is my parameter, EI is constant), (θ'' is the second derivative of theta with respect to arc length (s))
because my equation is a function of (s) rather than (x), i need to include the following equations to describe the cartesian coordinates:
x' = cosθ
y' = sinθ
All of this is written in a text file, which the program then runs. there is a section in the text file where i need to state the initial solutions for each of the following variables (θ, θ', x and y), but i do not understand what it is or how to find it. I have the 4 boundary conditions for this example:
(Beam length from zero to one)
θ'(0) = 0
θ'(1) = 0
x(0) = 0
y(1) = 0
Basically, what i am trying to ask is how to find the starting/initial solution to this system of ODE's? all i know is that the initial solution needs to be a function of the arc length (s)
Much thanks
I am using a program called AUTO 07p to solve ODE's but having some trouble in a certain part where i have to state the starting solution. I am computing buckling of a straight horizontal beam, using something called the elastica equation. to compute this, i use the following ODE's
θ'' + P/EI * sin θ = 0 (P is my parameter, EI is constant), (θ'' is the second derivative of theta with respect to arc length (s))
because my equation is a function of (s) rather than (x), i need to include the following equations to describe the cartesian coordinates:
x' = cosθ
y' = sinθ
All of this is written in a text file, which the program then runs. there is a section in the text file where i need to state the initial solutions for each of the following variables (θ, θ', x and y), but i do not understand what it is or how to find it. I have the 4 boundary conditions for this example:
(Beam length from zero to one)
θ'(0) = 0
θ'(1) = 0
x(0) = 0
y(1) = 0
Basically, what i am trying to ask is how to find the starting/initial solution to this system of ODE's? all i know is that the initial solution needs to be a function of the arc length (s)
Much thanks