AE202 Lecture 6 Symbolic Computation

AE202 Lecture 6 Symbolic Computation - AE202 Aerospace...

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AE202 Aerospace Flight Mechanics Lecture 6: Symbolic Computation
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Symbolic Computation MATLAB symbolic toolbox – lets you perform symbolic (algebraic) manipulations – uses MuPAD as its computer algebra systems (CAS) Allows you to perform: – Linear algebraic operations – Differentiation – Integration – Simplification – Transforms – Variable-precision arithmetic – Equation solving
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Symbolic Variables First must create symbolic variables – done with syms command, e.g. – creates 3 symbolic variables named a, b and c – also can use sym(‘someName‘) – can create symbolic numbers. • explicitly • from existing numeric variables syms a b c a = sym('alpha'); b = sym(6); c = sym(A);
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Symbolic Expressions Can create symbolic expressions – combinations of symbolic and numeric variables e.g. create symbolic variable to represent the Golden ratio now create a symbolic expression 15 2 >> rho = sym('(1 + sqrt(5))/2');   2 21 f >> f=2*rho^2+rho-1; f = 5^(1/2)/2 + 2*(5^(1/2)/2 + 1/2)^2 - 1/2 >> pretty(f) 1/2 / 1/2 \2 5 | 5 1 | 1 ---- + 2 | ---- + - | - - 2 \ 2 2 / 2
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Symbolic Expressions >> syms a b c x >> p1=a*x^2+b*x+c; 2 1 () p x ax bx c 2 2 p x dx ex f >> syms d e f >> p2=d*x^2+e*x+f; Consider 2 quadratic functions Can perform simple operations on them: addition / subtraction multiplication division, exp, sin, cos >> p1+p2 ans = c + f + b*x + e*x + a*x^2 + d*x^2 >>p1*p2 ans = (a*x^2 + b*x + c)*(d*x^2 + e*x + f)
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This note was uploaded on 01/26/2012 for the course AE AE 202 taught by Professor Martin during the Spring '09 term at University of Illinois, Urbana Champaign.

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AE202 Lecture 6 Symbolic Computation - AE202 Aerospace...

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