### Author:  [@Rafsing](https://discourse.processing.org/u/Rafsing)
#### Post date: [December 28, 2020, 1:55pm UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/1 "2020-12-28T13:55:50Z")
I want to simulate the nth level pendulum (double, triple and so on). I found the equations for the acceleration of the nth pendulum on this page: [https://www.researchgate.net/publication/336868500\_Equations\_of\_Motion\_Formulation\_of\_a\_Pendulum\_Containing\_N-point\_Masses](https://www.researchgate.net/publication/336868500_Equations_of_Motion_Formulation_of_a_Pendulum_Containing_N-point_Masses) but I am having trouble changing it to code. My main problem is that I don’t know where some of the indexes came from. Here’s the equation I’d like to change into code:
This is my code:
```auto
int sigma(int j, int k)
{
return int(j<=k);
}
int phi(int j, int k)
{
return int(!(j==k));
}
void calculateAcceleration()
{
float dividend = 1, divider = 0;
float[] copyAcceleration = new float[bob.size()];
for (int i = 0; i
### Author:  [@MiguelSanches](https://discourse.processing.org/u/MiguelSanches)
#### Post date: [December 28, 2020, 3:14pm UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/2 "2020-12-28T15:14:37Z")
Hi @Rafsing,
If I am not mistaken and didn’t commit any mistakes the following code should reproduce the equation
```auto
int n = 3;
float []m = {20, 20, 20};
float []l = {40, 40, 40};
float []angle = {PI/2, PI/2, PI/2};
float []vel = {0,0,0};
float []accel = {0,0,0};
void setup() {
float g = 1;
float den = 0;
float num1 = 0;
float num2 = 0;
float num3 = 0;
for (int j = 0; j < n; j++) {
//denominator
for (int k = 0; k < n; k++) {
den += m[k] * l[k] * l[k] * (j <= k? 1 : 0);
}
for (int k = 0; k < n; k++) {
//first numerator
num1 = g * l[j] * sin(angle[j]) * m[k] * (j <= k? 1 : 0);
//second numerator
float inner_sum = 0;
// inner sum
for (int q = k+1; q < n; q++) {
inner_sum += m[q] * (j <= q? 1 : 0);
}
num2 = inner_sum * l[j] * l[k] * sin(angle[j] - angle[k]) * vel[j] * vel[k];
//Third numerator
//The inner sum is the same as in the num2
num3 = inner_sum * l[j] * l[k] * (sin(angle[k] - angle[j]) * (vel[j] * vel[k]) * vel[k] + (j != k ? 1 : 0) * cos(angle[j] - angle[k])*accel[k]);
}
accel[j] = - (num1 + num2 + num3) / den;
}
printArray(accel);
}
```
Hope it helps
---
### Author:  [@MiguelSanches](https://discourse.processing.org/u/MiguelSanches)
#### Post date: [December 28, 2020, 4:52pm UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/3 "2020-12-28T16:52:38Z")
May I ask, where did you get that equation from?
I don’t think that is correct…
If you deduced it yourself from the equation below I can assure you that the one you posted is not correct, You can even check with a simple or double pendulum equation
For a simple pendulum:
Your denominator does not depend on the mass
For a double pendulum:
Your denominator must include cosine functions, which are not present in the equation you posted
---
### Author:  [@Rafsing](https://discourse.processing.org/u/Rafsing)
#### Post date: [December 28, 2020, 6:16pm UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/4 "2020-12-28T18:16:21Z")
I derived this equation from the equation number 38:
---
### Author:  [@MiguelSanches](https://discourse.processing.org/u/MiguelSanches)
#### Post date: [December 29, 2020, 8:45am UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/5 "2020-12-29T08:45:26Z")
I don’t think that is correct.
The last term also depends on the acceleration. Which if I am not mistaken takes into account the cosine function that is missing you. Notice that for a simple pendulum this last term is zero because j = k, hence phi is 0. But for a double pendulum, when j = 1, and k = 2, then the phi function became 1 and introduces the cosine functions.
---
### Author:  [@Rafsing](https://discourse.processing.org/u/Rafsing)
#### Post date: [December 29, 2020, 12:28pm UTC](https://discourse.processing.org/t/how-to-change-the-equation-into-a-code-in-an-nth-pendulum/26558/6 "2020-12-29T12:28:12Z")
How would you transform it then?