# Write a program to simluate multi object

1. Homework Statement
i want to simulate the object in space with c++

2. Homework Equations
i use a very small time interval to calculate the force and velocity.
i get wrong answer that the total energy in the system are increased.
And the objects are on the wrong locus.

Obj.Force = -g*m_1*m_2/(r*r);
Obj.Velocity += Obj.Force/mass *time;

3. The Attempt at a Solution

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D H
Staff Emeritus
You didn't give details on what you did, so I am guessing a bit here.
• How many objects do you have?
You need to address all pairs of objects.
• The gravitational force exerted on object 1 by object 2 is better written as
$$\mathbf F = -\,\frac {G m_1 m_2}{||\mathbf r_{2\to1}||^3||} \mathbf r_{2\to1}$$
• Object 1 exerts an equal but opposite force on object 2.
Do you have all masses moving in your simulation?
• If you simply compute the position and velocity at some time $t+\Delta t$ as $\mathbf r(t+\Delta t) = \mathbf r(t) + \Delta t \mathbf v(t)$ and $\mathbf v(t+\Delta t) = \mathbf v(t) + \Delta t \mathbf a(t)$ where $a(t)$ is the acceleration per Newton's laws you will get bad results. This is called the Euler method for propagating a differential equation.
Euler integration typically yields lousy results. You need to use a better integrator. Look into the verlet method, the velocity verlet (or Heun's method), and Runge-Kutta integration.

You didn't give details on what you did, so I am guessing a bit here.
• How many objects do you have?
You need to address all pairs of objects.
• The gravitational force exerted on object 1 by object 2 is better written as
$$\mathbf F = -\,\frac {G m_1 m_2}{||\mathbf r_{2\to1}||^3||} \mathbf r_{2\to1}$$
• Object 1 exerts an equal but opposite force on object 2.
Do you have all masses moving in your simulation?
• If you simply compute the position and velocity at some time $t+\Delta t$ as $\mathbf r(t+\Delta t) = \mathbf r(t) + \Delta t \mathbf v(t)$ and $\mathbf v(t+\Delta t) = \mathbf v(t) + \Delta t \mathbf a(t)$ where $a(t)$ is the acceleration per Newton's laws you will get bad results. This is called the Euler method for propagating a differential equation.
Euler integration typically yields lousy results. You need to use a better integrator. Look into the verlet method, the velocity verlet (or Heun's method), and Runge-Kutta integration.
Think you.
I found those methods in web.
i can't apply those method into my program
Can anyone help me?

D H
Staff Emeritus
You need to supply information on what you have done yourself before we can help you any further. And why to you claim you can't apply those methods to your program? Did you try?

You need to supply information on what you have done yourself before we can help you any further. And why to you claim you can't apply those methods to your program? Did you try?
int i,j,k;
long double temp = duration,t;
Object * oTemp = (Object *)malloc(sizeof(Object)*this->numObj);
Vector3D Temp,* a = (Vector3D *)malloc(sizeof(Vector3D)*this->numObj);
for(i = 0; i<this->numObj;i++)
{
oTemp.copy(this->objList);
a = this->objList->force/this->objList->mass;
}
while(temp > 0)
{
for(i = 0; i<this->numObj-1;i++)
{
for(j = i+1;j<this->numObj;j++)
{
Temp = this->objList->gForce(*this->objList[j]);
oTemp.force = oTemp.force + Temp;
oTemp[j].force = oTemp[j].force - Temp;
}
}

for(i = 0;i<this->numObj;i++)
{
Temp = oTemp.force/oTemp.mass;
oTemp.position = oTemp.position + oTemp.velocity *this->timeInt + gTemp*0.5*this->timeInt*this->timeInt +(Temp- a)*1/12*this->timeInt*this->timeInt*this->timeInt;
oTemp.velocity = oTemp.velocity + (oTemp.force + this->objList->force)/oTemp.mass/2* this->timeInt;

*this->objList = oTemp;
}
temp -= this->timeInt;
}

This is my program that corrected.
i change the highlighted code. it is correct?

Physic::Vector3D Physic::Object::gForce(const Physic::Object & param)
{
long double r;
Vector3D temp = this->delta(param);
r = !temp;
return temp.toNV()*gravityCon*this->mass*param.mass/(r*r*r);
}
temp.toNv() is return -(temp)

Last edited:
D H
Staff Emeritus
What kind of results do you get?

• As a general rule, it is a bad idea to use malloc in C++. Use new() instead.
• What are you doing here: "r = !temp;"

What kind of results do you get?

• As a general rule, it is a bad idea to use malloc in C++. Use new() instead.
• What are you doing here: "r = !temp;"
! = return sqrt(x*x+y*y+ z*z)
malloc is not good but i only found this method for undetemined size of array

D H
Staff Emeritus
! = return sqrt(x*x+y*y+ z*z)
Yikes. Operator overloading run amok! I assume that Vector3D is a class handed to you, rather than written by you. Overzealous use of operator overloading is widely viewed as a bad practice. Some view any use of operator overloading as a bad practice; the use of operator overloading is banned in many programming shops and requires a waiver in many more.

malloc is not good but i only found this method for undetemined size of array
Read up on new. Which of the two lines below is clearer?
Code:
Object * oTemp = (Object *)malloc(sizeof(Object)*this->numObj);
Object * oTemp = new Object[this->num_Obj)];
There is another big advantage of new over malloc. malloc merely allocates memory. The allocated memory will contain random garbage. new on the other hand invokes constructors for the object.