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April 25th, 2017, 06:53 AM  #1 
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations  Are Lagrangian simulations 100% accurate ?
Are Lagrangian simulations 100% accurate algebraically? When programming in a Lagrangian function for determining the position of objects in a system, are previous point values used when calculating new points? I am still struggling with lagrangian mathematics. I may need to step back to calculous. 
April 26th, 2017, 02:37 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out. 
I think in most practical cases your results are going to be approximate, otherwise we wouldn't bother with numerics. But likely there are contrived examples. And yes, it is typically the case that after a phase or state space is established (i.e., the system of equations governing the system), the 'future' values, depend on the previous values, along with some scaling factors and so on. 
April 29th, 2017, 06:47 AM  #3 
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations 
Damn. So I can't reverse a system and get the initial state.

April 29th, 2017, 05:47 PM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out. 
Umm. Depends on the system. What are you modelling ?

April 30th, 2017, 08:41 AM  #5 
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations 
1000's of particles. They can pass through each other. They are just points that pull on each other. 
April 30th, 2017, 05:35 PM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out. 
Is energy conserved in the system (do the particles undergo elastic collisions or exchange heat)? For nonequilibrium dynamics problems (NEMD), I think running backwards would be troublesome due to stability in your error. 
May 1st, 2017, 05:59 AM  #7  
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations  Quote:
... At some point int he simulation, energy may be added. From user input.  
May 1st, 2017, 06:10 AM  #8  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out.  Quote:
Yes sometimes we have a constant field applied to the system for various reasons. It's not always useful to think of physical examples when modelling abstract things, they tend to give the wrong impression. There is no ball that will mimic your reductionist model of interacting particles. Sent from my iPhone using Tapatalk  
May 1st, 2017, 08:44 AM  #9  
Member Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations 
Okay. I'm not trying to make a ball. I just didn't know what you meant by "elastic" collisions. Like classical physics at the human scale? I'm just trying to simulate pseudo particles. Quote:
Last edited by InkSprite; May 1st, 2017 at 08:47 AM.  
May 23rd, 2017, 04:52 AM  #10 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,722 Thanks: 600 Math Focus: Yet to find out. 
Yes pseudo particles would likely collide elastically in your simulation. This is a fairly unrealistic situation in the real world (except for the refraction of light maybe). But it stands as a good starting point. The 'fields' i was referring to could be thought of as a gradient which causes items in your simulation to have foccussing/defocussing effects. In that sense, they are 'moving'. However i assume you mean that these gradients could change with time or as specified by some function. 

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100%, accurate, lagrangian, simulations 
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