Classical mechanics -- Equations for simulating the motion of a body

[s1mos_tsr]

Hello forum, i want to make a samulation of a body. The body will be moved horisontal on y,x axis. I want on my simulation the body to change direction many times(for example i want to go for 10sec right and then left end right...). My question is does i need more than one differential equation to describe this type of motion?
thanks in advance lovers of physics

 

[BvU]

Hello @s1mos_tsr , !

What causes the body to move/change direction ?
As a minimum you don't need a differential equation at all, just a prescription for the motion...

 

[s1mos_tsr]

Lets say that the object has a inside mechanins to produce force, for example at t=0 a instand force make the object to move right and at t=10 a counterforce make the object to move left. In my mind i have a plan to make a dynamic model to have the simulation i don't know if this is the right method.

 

[berkeman]

Lets say that the object has a inside mechanins to produce force, for example at t=0 a instand force make the object to move right and at t=10 a counterforce make the object to move left. In my mind i have a plan to make a dynamic model to have the simulation i don't know if this is the right method.

Welcome to the PF.

Can you say a bit about your background so far in math and physics? Are you familiar with Newton's Laws of Motion?

https://en.wikipedia.org/wiki/Newton's_laws_of_motion

Are you familiar with drawing a Free Body Diagram (FBD) of an object to help in calculating the motion resulting from forces and torques ("moments") applied to the body?

 

[s1mos_tsr]

I am studying mechanical engineering and i started a project about control systems. My project is to make a simulation on MATLAB of an inverted pendulum but because its a little bit deep for me i wanted to start a easier simulation on MATLAB like a free fall body and moving body on surface. My goal is to achieve the control the pendulum. I want also to make it more visual and try to animate the simulation. I have good background on statics systems but on the dynamics models i am not so good. My main question this moment what i said at the 1st post and also how to describe with maths the change of force that makes the body to change direction.
** at t=0 a instand force make the object to move right and at t=10 a counterforce make the object to move left

 

[berkeman]

Well, if you use stepwise continuous vector forces, you can use the kinematic equations of motion for constant acceleration, which simplifies things a lot, right? Maybe start with that, and then later move on to discrete simulations of motion where the forces vary with time.

What would the motion of a 1kg mass be like given this piecewise continuous force profile?

$0s < t \leq 1s : F = 1N \hat x$
$1s < t \leq 2s : F = 3N \hat y$
$2s < t \leq 3s : F = -2N \hat x$

 

[s1mos_tsr]

Ok i think i get it a little bit. The point is to change the force(by changing the the sign) while the code is running at the time you want, correct me if i am wrong. But on the image i don't understand what N and X(hat) represents there.

 

[BvU]

$N$ is Newton, SI unit of force (kg m/s²)
$\hat x$ is a unit vector in the $x$-direction