Runge Kutta Motion with flexible body

I need someone to setup a Runge Kutta computation of the motion of a mass being moved by a flexible object.

The inputs to the problem are:

mass (the mass of the object to be moved)

stiffness_linkage (the spring rate of the linkage that moves the mass)

stiffness_return_spring (the spring rate of the return spring)

spring_static (the preload on the return spring)

damping (friction on the linkage)

Z() (an array of the designed actuation motion positions in uniform time increments)

Zd1(), Zd2(), Zd3() (The derivitives of the designed motion if you need them)

time_increment (the time between each value in the Z arrays)

The returns of the program are:

RZ() the response positions of the mass considering the flexible linkage.

RF() the response force

If you know an alternative solution to this problem beside RK, I may be interested.

I will be adding this code to a VB.net project so the code MUST be compatible with VB.net

I have a sample RK code but I don't know how to apply it. (Shown below)

I also have a sample solution to this problem that uses the Euler method, it works but I read the RK is more accurate, so I would like to see the difference but need help to replace the Euler code with RK code.

Dim k1, k2, k3, k4 As Double

Dim x, y, h As Double

Dim i As Long

x = 1

y = 10 ' These are the initial values of x & y

h = 0.1 ' This is the step size

For i = 1 To 5

k1 = h * f(x, y) ' eq(16a)

k2 = h * f(x + h / 2, y + k1 / 2) ' eq(16b)

k3 = h * f(x + h / 2, y + k2 / 2) ' eq(16c)

k4 = h * f(x + h, y + k3) ' eq(16d)

y = y + k1 / 6 + k2 / 3 + k3 / 3 + k4 / 6 ' eq(16)

x = x + h

[url removed, login to view]("when x = " & x & "y = " & y)

Next i

Function f(ByVal x, ByVal y) As Double

f = x ^ 2 + y

End Function

Teknik Matematika

ID Proyek: #799513

Tentang proyek