## 65 Reputation

2 years, 273 days

## How to draw an ellipse based on the equa...

Maple

Suppose H is a 2*2 matrix and (x0,y0) is the center of an ellipse. We want to draw the ellipse in form of (x-x0,y-y0)H(x-x0,y-y0)^T.

Equivalently, suppose we use variable P to show both x and y in the vector form. How is it possible to draw P^T H P? I would be thankful if you could give me and example.

## How to solve continuous time LQR optimal...

Suppose we have a "Finite-horizon, continuous-time LQR" optimal control problem. I am wondering how to solve Riccati DE and then determine state and control over time. Is it possible to analytically solve Riccati DEs? Suppose we have this example and we want to solve the problem based on the formulas in Wikipedia webpage.

A := Matrix(2, 2, [[2, 1], [1, -1]])

B := Vector[column](2, [3, 1])

Q := Matrix(2, 2, [[3, 0], [0, 2]])

R := 3

## How to solve the differential equation w...

Maple

I want to solve a differential equation with piecewise function, but I face an error. I am wondering how to handle it. Thanks

t[1]:=1

x := t -> piecewise(0 <= t and t < t[1], -60*t + 100, t[1] <= t and t <= 10, 1.645*sqrt(480*t))

dsolve({diff(p(t), t) = 2*h*x(t), p(T) = 0}, p(t))

and the error is :

"Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {pT = 0}"

 (1)

 (2)

## How to determine the summation of two pi...

Maple

I have two functions U1 and U2 which are both piecewise functions. I want to determine the function representing the summation or subtraction of these two functions, that is, U=U1-U2 or U=U1+U2.

alpha := 0.01;
alpha := 0.01
U1 := piecewise((1 - alpha)*lambda[1] - lambda[2] <= 0, 0, 0 < (1 - alpha)*lambda[1] - lambda[2], 5)
U2 := piecewise(-(1 + alpha)*lambda[1] + lambda[2] <= 0, 0, 0 < -(1 + alpha)*lambda[1] + lambda[2], 5)

Suppose we have U=U1-U2. I am wondering how to draw regions defined by function U and also how to label them.

## Can I use the license of Maple 2019 for ...

Maple 2020

Hello

I purchased the license of Maple 2019 and I am using the same version up to now. I am wondering if I download the latest version, can I use the former license? When I click on "check for updates" there is nothing for updating but when I want to run a Maple file written in the latest version, I face an error.

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