# Linear algebra and applications to aerospace

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1. Apr 14, 2015

### Istruggle

I am researching ways linear algebra is integrated into aerospace engineering (I know its alot). I am looking for specific ways.

Any help would be appreciated.

2. Apr 14, 2015

### Greg Bernhardt

What have you come up with so far?

3. Apr 14, 2015

### Istruggle

I already understand how linear algebra is applied to calculating the pitch of a plane. I was interested if there was an application for linear algebra for air flow. I find papers that mention it but don't really explain how its used to calculate the air flow. Any other suggestions are appreciated.

4. Apr 15, 2015

Linear algebra is the basis for most or all numerical methods of solving differential equations, so it's an integral part of CFD (or computational structures or dynamics, for that matter).

5. Apr 16, 2015

### SteamKing

Staff Emeritus
Indeed, you can't have finite element analysis without using linear algebra to solve the finite element equations.

6. Apr 24, 2015

### lonely_nucleus

cool profile picture friend. Do most students learn linear algebra before ordinary differential equations? Do you know any applications of linear algebra for nuclear engineering in general?

7. Apr 24, 2015

### SteamKing

Staff Emeritus
I should hope so.

I started learning about matrices and linear equations in eighth grade Algebra I. It's one of those subjects, like trig, which pops up now and then in the curriculum. It can be useful at solving problems without getting deep into the theory of LA. Knowledge of calculus is absolutely not required.

8. Apr 26, 2015

Most engineering curricula that I know of place linear algebra after differential equations, though usually people have taken some form. Basic linear algebra previously, typically in "Algebra 2", I believe. That is typically enough to get by in a basic differential equations course. Any more advanced differential equations courses or numerical methods courses would typically come after a full linear algebra course.

9. May 11, 2015

### DuncanM

One application that comes to mind quickly is the analysis of aeroelasticity and flutter. By forming the appropriate matrix, and computing its eigenvalues and eigenvectors, you can determine the modes of vibration, and its frequencies.

I suppose that would fall under the general rubric of structures.

Same for the stability of the aircraft or spacecraft: form the appropriate matrix, compute its eigenvalues and eigenvectors, and you'll know how stable the system is.