Linear system in polar coordinates

[Jhenrique]

Hellow! I have searched for some theory about linear system in polar coordinates, unfortunately, I not found anything... exist some theory, some book, anything about this topic for study? Thanks!

 

[Stephen Tashi]

Give an example of what you mean by "linear system in polar coordinates". Are you talking about a set of simultaneous linear equations? - or a system of linear differential equations?

 

[Jhenrique]

I think in something like:
[tex]\begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} r\\ \theta\\ \end{bmatrix} = \begin{bmatrix} b_{1}\\ b_{2}\\ \end{bmatrix}[/tex]
Where a_ij can be a simple coeficient or a polynomial of kind aD³+bD²+cD+d (where D is the derivative operator) and b_i a simple coeficient.

But using [r θ] instead of use [x y].

 

[Stephen Tashi]

Where a_ij can be a simple coeficient or a polynomial of kind aD³+bD²+cD+d (where D is the derivative operator) and b_i a simple coeficient.

In that equation, I don't understand what function D would operate upon? Do we have funtions [itex] r = r(t), \theta = \theta(t) [/itex] and [itex] D = \frac{d}{dt} [/itex] ?

 

[CellCoree]

Hello there! I can assure you that there is indeed a theory about linear systems in polar coordinates. This topic falls under the field of mathematics called coordinate geometry, which deals with the study of geometric figures and their properties using different coordinate systems, including polar coordinates.

There are various books and resources available that discuss this topic in detail. Some recommended books are "Coordinate Geometry" by Loney, "Analytic Geometry" by Love and Rainville, and "Calculus with Analytic Geometry" by Simmons. You can also find online lectures and tutorials on this subject.

In linear systems, we use polar coordinates to describe the relationship between two variables, such as distance and angle. This coordinate system is particularly useful in problems involving circular or rotational motion, as well as in engineering and physics applications.

I hope this information helps you in your study. Happy learning!