gibson:teaching:fall-2012:math445:pf1-solns
====== Differences ====== This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
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gibson:teaching:fall-2012:math445:pf1-solns [2012/12/11 14:19] gibson |
gibson:teaching:fall-2012:math445:pf1-solns [2012/12/11 14:22] (current) gibson |
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| </latex> | </latex> | ||
| - | So $dx/dt = [x_2, -g - \mu x_2 |x_2|]$ | + | So $dx/dt = [x_2, ~-g - \mu x_2 |x_2|]$ |
| Line 239: | Line 239: | ||
| from the initial conditions $x(0) = [y(0), ~v_y(0)] = [0, 0]$. | from the initial conditions $x(0) = [y(0), ~v_y(0)] = [0, 0]$. | ||
| + | <code> | ||
| g = 9.81; | g = 9.81; | ||
| mu = 0.35; | mu = 0.35; | ||
| f = @(x) [x(2) ; -g - mu*x(2)*abs(x(2)]; | f = @(x) [x(2) ; -g - mu*x(2)*abs(x(2)]; | ||
| - | [t, x] = ode45(f, 0:100, [0 ; 0]); | + | [t, X] = ode45(f, 0:100, [0 ; 0]); |
| + | </code> | ||
| Line 250: | Line 251: | ||
| Label the axes. | Label the axes. | ||
| - | plot(t, x(:,1)) % first column of x is 1st component of x as a function of time | + | plot(t, X(:,1)) % first column of returned X is 1st component of x as a function of time |
| xlabel('t') | xlabel('t') | ||
| ylabel('y = height of ball') | ylabel('y = height of ball') | ||
| Line 277: | Line 278: | ||
| of A. | of A. | ||
| + | <code> | ||
| function y = sparse_matvec_mult(A,x) | function y = sparse_matvec_mult(A,x) | ||
| K = nnz(A); | K = nnz(A); | ||
| Line 288: | Line 290: | ||
| end | end | ||
| end | end | ||
| + | </code> | ||
gibson/teaching/fall-2012/math445/pf1-solns.1355264399.txt.gz · Last modified: 2012/12/11 14:19 by gibson
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