Equation of 3D motion with V, An, R

Hello masters! I have an equation of x, y. Calculate the velocities in x(vx) and y(vy). Continue to calculate the acceleration in x(ax) and y(ay). Calculate velocity magnitude (v), acceleration magnitude (a), tangential acceleration magnitude (at), normal acceleration magnitude (an), curvature radius (R) over time from 0 to 5s . And finally draw the trajectory. However I had some trouble writing matlab code and didn't know how to draw trajectory.

function ptcd_ptqd
clc
clear var1
clear var2
close all

%% Input
t = linspace(0,5,6);

%% Calculate coordinates
x = 3*t.^2-(4/3*t.^3) ; 
y = 8*t ; 

dt = diff(t);
dx = diff(x);
dy = diff(y);
%% Calculate velocity magnitude
vx = dx./dt ;
v = sqrt(vx.^2+vy.^2); 
dvx = diff(vx);
dvy = diff(vy);
%% Calculate acceleration magnitude
ax = dvx./dt;  
a = sqrt(ax.^2+ay.^2);
end

Answer 1

[Alan Stevens]

A little more like this perhaps, since you are given explicit expressions for velocities and accelerations (though note that ax should be 6 - 8t, not 6 - 4t):

x = @(t) 3*t.^2 - 4*t.^3/3;
vx = @(t) 6*t - 4*t.^2;
ax = @(t) 6 - 8*t;
y = @(t) 8*t;
vy = @(t) 8;
ay = @(t) 0;

t = linspace(0,5,100);
v = sqrt(vx(t).^2 + vy(t).^2);
a = sqrt(ax(t).^2 + ay(t).^2);
at = abs(diff(v)./diff(t));
an = sqrt(abs(a(1:end-1).^2 - at.^2));
R = v(1:end-1).^2./an;

plot(x(t),y(t)),grid
xlabel('x'),ylabel('y')

[Luyen Tran]

Thanks Alan Stevens! but I was given only x and y equations

[Alan Stevens]

Ok, but they are simple to differentiate. Instead of defining x, y etc as functions, you could specify the values of t first, then simply calculate corresponding values of x, y etc, using diff for the derivatives. Note that each time you use diff, you reduce the length of the vector by 1.