Trying to Differentiate Parametric Equation, Error "Error using diff Difference order N must be a positive integer scalar."

I am trying to differentiate X_Rotor and Y_Rotor with respect to v. When i try to using diff() it give the following error code

"Error using diff

Difference order N must be a positive

integer scalar."

I am also trying to graph the parametric equations, and lines are connecting my points. Not sure why? When i graph across 2*PI this is the figure i get.

When graphing across only the time point i want this is what i get.

Not sure why the straight lines are connecting those points. Anything helps thanks!!

This is my code below:

% Define symbolic variables
syms R Z e v real

% Define parameters
Z = 3;      %Lobes
R = 10;     % Set the value of R
e = 1.5;    % Set the eccentricity value

% Define intervals for v
v1 = linspace(pi/6, pi/2, 100);          % First range: pi/6 to pi/2
v2 = linspace(5*pi/6, 7*pi/6, 100);      % Second range: 5pi/6 to 7pi/6
v3 = linspace(3*pi/2, 11*pi/6, 100);     % Third range: 3pi/2 to 11pi/6
alpha = linspace(0,2*pi,1000);
v = linspace(0, 2*pi,1000);
% Concatenate v
%v = [v1, v2, v3];

% W is defined as to simplify equations
w = 2 * e * sqrt(1 - (Z*e/R)^2 .* sin(Z * v).^2) .* cos(Z * v);

% Parametric equations
X_Rotor = R * cos(2 * v) - (Z*e.^2 / R) .* sin(2 * Z * v) .* sin(2 * v) + w .* cos(2 * v) - 1.5;
Y_Rotor = R * sin(2 * v) + (Z*e.^2 / R) .* sin(2 * Z * v) .* cos(2 * v) + w .* sin(2 * v);

X_Housing = R * cos(alpha) + e * cos(alpha*Z);
Y_Housing = R * sin(alpha) + e * sin(alpha*Z);

% Plot the curve for specified ranges
figure;
plot(X_Rotor, Y_Rotor, 'r', X_Housing, Y_Housing, 'b');
title('Parametric Plot of the Rotor Curve for Specific Intervals');
xlabel('X');
ylabel('Y');
grid on;
axis equal;

% Derivatives of X and Y with respect to v
dXdv = diff(X, v);
dYdv = diff(Y, v);

[Walter Roberson]

dXdv = diff(X, v);

X is not defined at that point.

Answer 1

[Walter Roberson]

syms R Z e v real

You declare v as symbolic

v = linspace(0, 2*pi,1000);

You overwrite v as numeric.

Answer 2

[Steven Lord]

At the start of your code you defined v as a symbolic variable.

% Define symbolic variables
syms R Z e v real

But then later in the code, you redefined it to be a numeric vector.

v = linspace(0, 2*pi,1000);

You then tried to use it as a symbolic variable at the end of the code.

% Derivatives of X and Y with respect to v
dXdv = diff(X, v);
dYdv = diff(Y, v);

But it's not a symbolic variable anymore.

There's another problem that I'm assuming is an artifact of you omitting part of your code for posting to Answers, nowhere does your code define either X or Y. You define variables whose names start with X and Y, but that's different.

Answer 3

[Star Strider]

Your diff call is not going to produce the result you want.

% Define symbolic variables
syms R Z e v real

% Define parameters
Z = 3;      %Lobes
R = 10;     % Set the value of R
e = 1.5;    % Set the eccentricity value

% Define intervals for v
v1 = linspace(pi/6, pi/2, 100);          % First range: pi/6 to pi/2
v2 = linspace(5*pi/6, 7*pi/6, 100);      % Second range: 5pi/6 to 7pi/6
v3 = linspace(3*pi/2, 11*pi/6, 100);     % Third range: 3pi/2 to 11pi/6
alpha = linspace(0,2*pi,1000);
v = linspace(0, 2*pi,1000);
% Concatenate v
%v = [v1, v2, v3];

% W is defined as to simplify equations
w = 2 * e * sqrt(1 - (Z*e/R)^2 .* sin(Z * v).^2) .* cos(Z * v);

% Parametric equations
X_Rotor = R * cos(2 * v) - (Z*e.^2 / R) .* sin(2 * Z * v) .* sin(2 * v) + w .* cos(2 * v) - 1.5;
Y_Rotor = R * sin(2 * v) + (Z*e.^2 / R) .* sin(2 * Z * v) .* cos(2 * v) + w .* sin(2 * v);

X_Housing = R * cos(alpha) + e * cos(alpha*Z);
Y_Housing = R * sin(alpha) + e * sin(alpha*Z);

% Plot the curve for specified ranges
figure;
plot(X_Rotor, Y_Rotor, 'r', X_Housing, Y_Housing, 'b');
title('Parametric Plot of the Rotor Curve for Specific Intervals');
xlabel('X');
ylabel('Y');
grid on;
axis equal;

% Derivatives of X and Y with respect to v
% dXdv = diff(X, v);
% dYdv = diff(Y, v);

Since neither ‘X’ or ‘Y’ appear to exist, however ‘v’ is a numeric vector, so I assume that you want to take the numeric derivative. That is most easily done using the gradient funciton, for example:

dXdv = gradient(X, v);

dYdv = gradient(Y, v);

or in earlier versions:

dXdv = gradient(X) ./ gradient(v);

dYdv = gradient(Y) ./ gradient(v);

The second argument to diff must be a scalar if you are calculating the symbolic derivative.

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