# Please help me put this into a proper for loop, using increments

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Hi, I am not very good with loops, so I did it be hand for 4 steps and then put them into code, I need somehow to put rFinal into a for loop so goes through 1000 times. I tried to do that, but without success, the loop are very incorrect, but I'm not sure how to fix them Use for reference, the variable status in order: Initial, Next, changed, New, Final Also NOTE: Pi in this case is the velocity not the variable "pi" (had to use variable pi..)

NOTE: the part I need help with is at the bottom (*** after the space), right BEFORE THE FOR LOOP, the rest is just variables if you want to run it.... if true %% Defining the variables

% the masses

M1=606; % galactic mass unit, = 2.32e7 of solar masses % central mass constants

M2=3690; % disk constants

M3=4615; % halo constants

% the radii and distances

rInitial=8.499; % kpc

rMin=3.51; % kpc

rMax=9.15; % kpc

a2=5.3178; % disk constants % scalar lengths

a3=12; % halo constants % scalar lengths

b1=0.3873; % central mass constants % scalar lengths

b2=0.25; % disk constants % scalar lengths

z=0;

% other remining variables and constants

PiInitial=6.827; % kpc/gtm

dt=1e-3; %time step

%%the order of solving the variables - done by hand

DeltarInitial= PiInitial*dt

rNext= rInitial + DeltarInitial

% solving for rChanged:

% partials of Fi1 % the acceleration components - with r initial

DiyFi1OverRInitial= (M1*rInitial) *dt / ( (b1^2+rInitial^2+z^2)^(3/2) );

% partials of Fi2 % the acceleration components - with r initial

DiyFi2OverRInitial= (M2*rInitial) *dt / ( (rInitial^2+( (a2+sqrt(b2^2+z^2))^2) )^(3/2) );

% partials of Fi3 % the acceleration components - with r initial

DiyFi3OverRInitialTerm1= ( 1.02*M3*rInitial*( (sqrt(rInitial^2+z^2) *dt / a3)^2.04 ) ) / (a3*(rInitial^2+z^2)*( 1+( (sqrt(rInitial^2+z^2) / a3)^1.02 )^2 ));

DiyFi3OverRInitialTerm2= ( M3*rInitial*( ( sqrt(rInitial^2+z^2) / a3 )^2.02 ) ) *dt / ( ( (rInitial^2+z^2)^(3/2) )*( 1+( ( sqrt(rInitial^2+z^2) / a3 )^1.02 ) ) );

DiyFi3OverRInitialTerm3= ( -2.02*M3*rInitial*( ( sqrt(rInitial^2+z^2) / a3 )^1.01 ) ) *dt / ( a3*(rInitial^2+z^2)*( 1+( ( sqrt(rInitial^2+z^2) / a3 )^1.02 ) ) ); % a negative term

DiyFi3OverRInitial= DiyFi3OverRInitialTerm1 + DiyFi3OverRInitialTerm2 + DiyFi3OverRInitialTerm3;

% the acceraration component in the r direction

arInitial= DiyFi1OverRInitial + DiyFi2OverRInitial + DiyFi3OverRInitial

PiNext=PiInitial + arInitial*dt

DeltarNext= PiNext*dt

rChanged= rNext + DeltarNext

% sloving for rNew:

% partials of Fi1 % the acceleration components - with rNext

DiyFi1OverRNext= (M1*rNext) *dt / ( (b1^2+rNext^2+z^2)^(3/2) );

% partials of Fi2 % the acceleration components - with rNext

DiyFi2OverRNext= (M2*rNext) *dt / ( (rNext^2+( (a2+sqrt(b2^2+z^2))^2) )^(3/2) );

% partials of Fi3 % the acceleration components - with rNext

DiyFi3OverRNextTerm1= ( 1.02*M3*rNext*( (sqrt(rNext^2+z^2) *dt / a3)^2.04 ) ) / (a3*(rNext^2+z^2)*( 1+( (sqrt(rNext^2+z^2) / a3)^1.02 )^2 ));

DiyFi3OverRNextTerm2= ( M3*rNext*( ( sqrt(rNext^2+z^2) / a3 )^2.02 ) ) *dt / ( ( (rNext^2+z^2)^(3/2) )*( 1+( ( sqrt(rNext^2+z^2) / a3 )^1.02 ) ) );

DiyFi3OverRNextTerm3= ( -2.02*M3*rNext*( ( sqrt(rNext^2+z^2) / a3 )^1.01 ) ) *dt / ( a3*(rNext^2+z^2)*( 1+( ( sqrt(rNext^2+z^2) / a3 )^1.02 ) ) ); % a negative term

DiyFi3OverRNext= DiyFi3OverRNextTerm1 + DiyFi3OverRNextTerm2 + DiyFi3OverRNextTerm3;

% the acceraration component in the r direction

arNext= DiyFi1OverRNext + DiyFi2OverRNext + DiyFi3OverRNext

PiChanged=PiNext + arNext*dt

DeltarChanged= PiChanged*dt

rNew= rChanged + DeltarChanged

%

%

%

% sloving for rFinal: - THE LOOP PART******************************************

% partials of Fi1 % the acceleration components - with rChanged

DiyFi1OverRChanged= (M1*rChanged) *dt / ( (b1^2+rChanged^2+z^2)^(3/2) );

% partials of Fi2 % the acceleration components - with rNext

DiyFi2OverRChanged= (M2*rChanged) *dt / ( (rChanged^2+( (a2+sqrt(b2^2+z^2))^2) )^(3/2) );

% partials of Fi3 % the acceleration components - with rNext

DiyFi3OverRChangedTerm1= ( 1.02*M3*rChanged*( (sqrt(rChanged^2+z^2) *dt / a3)^2.04 ) ) / (a3*(rChanged^2+z^2)*( 1+( (sqrt(rChanged^2+z^2) / a3)^1.02 )^2 ));

DiyFi3OverRChangedTerm2= ( M3*rChanged*( ( sqrt(rChanged^2+z^2) / a3 )^2.02 ) ) *dt / ( ( (rChanged^2+z^2)^(3/2) )*( 1+( ( sqrt(rChanged^2+z^2) / a3 )^1.02 ) ) );

DiyFi3OverRChangedTerm3= ( -2.02*M3*rChanged*( ( sqrt(rChanged^2+z^2) / a3 )^1.01 ) ) *dt / ( a3*(rChanged^2+z^2)*( 1+( ( sqrt(rChanged^2+z^2) / a3 )^1.02 ) ) ); % a negative term

DiyFi3OverRChanged= DiyFi3OverRChangedTerm1 + DiyFi3OverRChangedTerm2 + DiyFi3OverRChangedTerm3;

% the acceraration component in the r direction

arChanged= DiyFi1OverRChanged + DiyFi2OverRChanged + DiyFi3OverRChanged

PiNew=PiChanged + arChanged*dt

DeltarNew= PiNew*dt

rFinal= rNew + DeltarNew

for i=1:5

arChanged= DiyFi1OverRChanged + DiyFi2OverRChanged + DiyFi3OverRChanged

arChanged= arChanged + 1

for i=1:5

PiNew(i)=PiChanged + arChanged*dt

for k=1:5

DeltarNew(k)= PiNew*dt

for i=1:5

rFinal(i)= rNew + DeltarNew

end

end

end

end

end

end

##### 6 Comments

sixwwwwww
on 7 Dec 2013

### Accepted Answer

sixwwwwww
on 7 Dec 2013

The part after *************** can be written in loop as follow:

DiyFi1OverRChanged= (M1 * rChanged) * dt / ( (b1^2+rChanged^2+z^2)^(3/2) );

DiyFi2OverRChanged= (M2*rChanged) *dt / ( (rChanged^2+( (a2+sqrt(b2^2+z^2))^2) )^(3/2) );

DiyFi3OverRChangedTerm1= ( 1.02*M3*rChanged*( (sqrt(rChanged^2+z^2) *dt / a3)^2.04 ) ) / (a3*(rChanged^2+z^2)*( 1+( (sqrt(rChanged^2+z^2) / a3)^1.02 )^2 ));

DiyFi3OverRChangedTerm2= ( M3*rChanged*( ( sqrt(rChanged^2+z^2) / a3 )^2.02 ) ) *dt / ( ( (rChanged^2+z^2)^(3/2) )*( 1+( ( sqrt(rChanged^2+z^2) / a3 )^1.02 ) ) );

DiyFi3OverRChangedTerm3= ( -2.02*M3*rChanged*( ( sqrt(rChanged^2+z^2) / a3 )^1.01 ) ) *dt / ( a3*(rChanged^2+z^2)*( 1+( ( sqrt(rChanged^2+z^2) / a3 )^1.02 ) ) ); % a negative term

DiyFi3OverRChanged= DiyFi3OverRChangedTerm1 + DiyFi3OverRChangedTerm2 + DiyFi3OverRChangedTerm3;

arChanged= DiyFi1OverRChanged + DiyFi2OverRChanged + DiyFi3OverRChanged;

PiNew(1) = PiChanged + arChanged * dt;

DeltarNew(1) = PiNew(1) * dt;

rFinal(1) = rNew + DeltarNew(1);

for i=1:5

arChanged= arChanged + 1;

PiNew(i + 1)= PiChanged + arChanged * dt;

DeltarNew(i + 1)= PiNew(i + 1) * dt;

rFinal(i + 1)= rNew + DeltarNew(i + 1);

end

It it what you need?

##### 6 Comments

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