Why doesn't diff() recognise the second variable?

syms x(t) m1 m2
xr = x;
xl = 0;
T = (m1 * diff(xl)^2) / 2 + (m2 * (diff(xr)^2)) / 2 % why doesn't it recognise that xr is a function of time?

Why is the different from this?

T = (m1 * diff(xl,t)^2) / 2 + (m2 * (diff(xr,t)^2)) / 2 % gives the expected result

whereas if i do

diff(xr) % it gives me the correct result?

What is going on here?

Answer 1

[Star Strider]

This works correctly in R2020a (Update 3):

syms x(t) 
xr = x
diff(xr) % why doesn't it recognise that xr is a function of time?
T = diff(xr)

producing:

xr(t) =
x(t)
 
ans(t) =
diff(x(t), t)
 
T(t) =
diff(x(t), t)

I cannot reproduce the error.

[madhan ravi]

Star could you try this and confirm ?

 T = (m1 * diff(xl)^2) / 2 + (m2 * (diff(xr)^2)) / 2

[Star Strider]

Sure!

syms x(t) m1 m2 xl(t) 
xr = x;
T = (m1 * diff(xl)^2) / 2 + (m2 * (diff(xr)^2)) / 2

produces:

T(t) =
(m2*diff(x(t), t)^2)/2 + (m1*diff(xl(t), t)^2)/2

Note the additions to the syms call.

EDIT —

Adding the edited changes:

syms x(t) m1 m2 
xr = x;
xl = 0;
T = (m1 * diff(xl)^2) / 2 + (m2 * (diff(xr)^2)) / 2

produces:

T(t) =
[ empty sym ]

most likely because the derivative of a scalar (without specifying the independent variable it is to be differentiated with respect to) does not exist:

Dxl = diff(xl)

produces:

Dxl =
     []

however:

Dxl = diff(xl,t) 

produces:

Dxl =
0

.

[madhan ravi]

Sorry for the mess Star, I had two tabs open used a wrong tab to submit the question, I mean for this one:

syms x(t) m1 m2
xr = x;
xl = 0;
T = (m1 * diff(xl)^2) / 2 + (m2 * (diff(xr)^2)) / 2 % it returns empty sym in my version :(

Produces:

T(t) =
 
[ empty sym ]

Edit: Ah now it's clear adding an empty array to another number gives an empty array, hence it was subtle and surprising.

Thank you Star!

[Star Strider]

As always, my pleasure!