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JolleJ
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3-dimensional parametric equations [Updated]
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Well, my problem is that I need to give some examples on 3-dimensional parametric equations. So far I've found out what parametric equations are, and more specifically what 3-dimensional parametric equations are. But now I am being asked to give some real-world examples of these.
A 3-dimensional parametric equations is an equation of something in a 3d-coordinate system, where each coordinate x,y,z are expressed by the same parameter t: x(t) = f1(t) ^ y(t) = f2(t) ^ z(t) = f3(t)
Well, so far I've found out that Solar Winds, Aurorae and the movement of the plasma inside a Tokamak are all 3-dimensional parametric equations. My problem is that while I know that the movements can be expressed by 3-dimensional parametric equations, I have absolutely no idea how these equations look like. I've searched all around the Internet, but I can't find any equations for this - or anything at all that looks like it.
I hope you can help.
Thanks in advance.
Update:
I have now advanced a bit, and acutally found a simulation of the particles moving inside a tokamak, which shows that the particles drift up or down depending on their charge q. So now I have a new problem:
My problem is now that I do understand the mathematics / physics equations used in the simulations.
The simulations starts with introducing all the varibles and functions:
After this, it makes a loop which constantly calculates the integrated function of "tokamak" (why this?). And after this adding the timedifference dt to the time variable t:
Loop:
I can see the that function det, is finding the determinant, though I do not know why this is relevant.
All of it is something with vectors, but I am not sure how.
Tried looking at it so long, but I am not good enough at vectors and integration yet, so I simply cannot see excacly what is going on.
I really hope that one of you can open my eyes.
Thanks in advance.
Look lower for update...
Homework Statement
Well, my problem is that I need to give some examples on 3-dimensional parametric equations. So far I've found out what parametric equations are, and more specifically what 3-dimensional parametric equations are. But now I am being asked to give some real-world examples of these.
Homework Equations
A 3-dimensional parametric equations is an equation of something in a 3d-coordinate system, where each coordinate x,y,z are expressed by the same parameter t: x(t) = f1(t) ^ y(t) = f2(t) ^ z(t) = f3(t)
The Attempt at a Solution
Well, so far I've found out that Solar Winds, Aurorae and the movement of the plasma inside a Tokamak are all 3-dimensional parametric equations. My problem is that while I know that the movements can be expressed by 3-dimensional parametric equations, I have absolutely no idea how these equations look like. I've searched all around the Internet, but I can't find any equations for this - or anything at all that looks like it.
I hope you can help.
Thanks in advance.
Update:
I have now advanced a bit, and acutally found a simulation of the particles moving inside a tokamak, which shows that the particles drift up or down depending on their charge q. So now I have a new problem:
Homework Statement
My problem is now that I do understand the mathematics / physics equations used in the simulations.
The simulations starts with introducing all the varibles and functions:
Code:
B0:=1
v,m:=1,.01
x,y,z:=3,0,0
vx,vy,vz:=v,v*q,0
t,dt:=0,.01
Integratemethod:=RK4
func det(a,b,c,d)
return a*d - b*c
endfunc
func R(x,y)
return (x^2+y^2)
endfunc
func acc(va,vb,ba,bb)
return (va*bb-vb*ba)/m
endfunc
func Bx(x,y,z)
return y*B0/R(x,y)
endfunc
func By(x,y,z)
return -x*B0/R(x,y)
endfunc
func Bz(x,y,z)
return 0
endfunc
Model tokamak
x':=vx
y':=vy
z':=vz
vx':=q*det(vy,vz,By(x,y,z),Bz(x,y,z))/m
vy':=q*det(vz,vx,Bz(x,y,z),Bx(x,y,z))/m
vz':=q*det(vx,vy,Bx(x,y,z),By(x,y,z))/m
endmodel
After this, it makes a loop which constantly calculates the integrated function of "tokamak" (why this?). And after this adding the timedifference dt to the time variable t:
Loop:
Code:
integrate tokamak(t,dt)
t:=t+dt
Homework Equations
I can see the that function det, is finding the determinant, though I do not know why this is relevant.
All of it is something with vectors, but I am not sure how.
The Attempt at a Solution
Tried looking at it so long, but I am not good enough at vectors and integration yet, so I simply cannot see excacly what is going on.
I really hope that one of you can open my eyes.
Thanks in advance.
Last edited: