Submitted by: Submitted by ihgonzalez
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Pages: 5
Category: Science and Technology
Date Submitted: 07/18/2016 01:24 PM
MATLAB ROLL EQUATIONS VERIFICATION
1. Tangential Component of Gravitational Vector Equation
gt = (((Vg*g)/((Vgab)^2)) * Vg);
MATLAB coding:
clear
clc
close all
syms gt Vgab VN VE VD g Vg go
Vg = [VN VE VD];
Vmag = sqrt(VN^2+VE^2+VD^2)
g = [0;0;go];
C = Vg*g;
U = [VN VE VD]* [0; 0; VD*go]
Vmag1 = Vmag^2
gt = ((U)/(Vmag1));
Results MATLAB:
gt = (VD^2*go)/(VD^2 + VE^2 + VN^2)
2. Normal Component of Gravitacional Vector
gn = g – gt
MATLAB coding:
clear
clc
close all
syms gt Vgab VN VE VD g Vg go gn
Vg = [VN VE VD];
Vgab = sqrt(VN^2+VE^2+VD^2)
g = [0 0 go];
gt = ([0 0 VD^2*go])/(VD^2 + VE^2 + VN^2)
gn = g - gt
Results MATLAB:
gn =
[ 0, 0, go - (VD^2*go)/(VD^2 + VE^2 + VN^2)]
Further Simplification by hand
= (go(VE^2 +VN^2))/VD^2 + VE^2 + VN^2
3. Tangential Component of Acceleration Vector Equation
At = ((Vg*Ag)/Vmag^2)* Vg
MATLAB coding:
clear
clc
close all
syms AN AE AD VN VE VD Vg Vmag At
Vg = [VN VE VD];
Vmag = sqrt(VN^2+VE^2+VD^2);
Ag = [AN AE AD];
C = Vg.*Ag
K = C.*Vg
At = (K)/(sqrt(VN^2+VE^2+VD^2))^2
Results MATLAB:
At =
[ (AN*VN^2)/(VD^2 + VE^2 + VN^2), (AE*VE^2)/(VD^2 + VE^2 + VN^2), (AD*VD^2)/(VD^2 + VE^2 + VN^2)]
4. Normal Component of Acceleration Vector
An = Ag – At
MATLAB coding:
clear
clc
close all
syms AN AE AD VN VE VD Vg Vmag At
Vg = [VN VE VD];
Vmag = sqrt(VN^2+VE^2+VD^2);
Ag = [AN AE AD];
C = Vg.*Ag
K = C.*Ag
At = (K)/(sqrt(VN^2+VE^2+VD^2))^2
An = Ag - At
Results MATLAB:
An =
[ AN - (AN*VN^2)/(VD^2 + VE^2 + VN^2), AE - (AE*VE^2)/(VD^2 + VE^2 + VN^2), AD - (AD*VD^2)/(VD^2 + VE^2 + VN^2)]
Simplify by hand
[ AN(VD^2 + VE^2 )/ (VD^2 + VE^2 + VN^2), AE(VD^2+VN^2)/ (VD^2 + VE^2 + VN^2),AD(VE^2+VN^2)/ (VD^2 + VE^2 + VN^2)]
5. Lift Vector
l = An - gn
MATLAB coding:
clear
clc
close all
syms AN AE AD VN VE VD Vg Vmag At l
syms gt g go gn
g = [0 0 go];
gt = ([0 0 VD^2*go])/(VD^2 + VE^2 + VN^2)
gn = g - gt
Vg = [VN VE VD];
Vmag =...