|
|
| Line 7: |
Line 7: |
| // Label f; | | // Label f; |
| // f.p=fontsize(6); | | // f.p=fontsize(6); |
| // xaxis(0,3);
| | xaxis(-1,2); |
| // yaxis(0,1.5);
| | yaxis(-1,2); |
|
| |
|
| // real f1(real x) { return 1 - erf(5x); }
| | real f1(real x) { return 3/2 * sin(pi/4 * (x - 1)) + 1/2; } |
|
| |
|
| for (int i = 0; i < 3; ++i) {
| | draw(graph(f1,-1,2),MidArrow); |
| draw((3*i,0)--((3*i,0)+dir(0))--((3*i,0)+dir(60))--cycle);
| | draw((0,0)--(1,f1(1)),EndArrow); |
| draw((3*i,-2)--((3*i,-2)+dir(0))--((3*i,-2)+dir(60))--cycle);
| |
| }
| |
|
| |
|
| draw((1.5,0.4)--(2.5,0.4),EndArrow); draw((4.5,0.4)--(5.5,0.4),EndArrow);
| | dot((0,0)); |
| draw((1.5,-1.6)--(2.5,-1.6),EndArrow); draw((4.5,-1.6)--(5.5,-1.6),EndArrow);
| | label("$O$",(0,0),NW); |
| | | label("$\mathbf{r}(t)$",(0.5,f1(1)/2),NNW); |
| dot((0,0),red); dot((0,0)+dir(0),darkgreen); dot((0,0)+dir(60),blue);
| |
| dot((3,0),red); dot((3,0)+dir(0),blue); dot((3,0)+dir(60),darkgreen);
| |
| dot((6,0),blue); dot((6,0)+dir(0),red); dot((6,0)+dir(60),darkgreen);
| |
| dot((0,-2),red); dot((0,-2)+dir(0),darkgreen); dot((0,-2)+dir(60),blue);
| |
| dot((3,-2),darkgreen); dot((3,-2)+dir(0),red); dot((3,-2)+dir(60),blue);
| |
| dot((6,-2),darkgreen); dot((6,-2)+dir(0),blue); dot((6,-2)+dir(60),red);
| |
| | |
| label("$r_1\circ r_2$",(-1,0.4),W); label("$r_2\circ r_1$",(-1,-1.6),W); | |
| label("$\rho_1$",(8,0.4),E); label("$\rho_2$",(8,-1.6),E); | |
| label("$r_2$",(2,0.4),N); label("$r_1$",(5,0.4),N);
| |
| label("$r_1$",(2,-1.6),N); label("$r_2$",(5,-1.6),N);
| |
| </asy> | | </asy> |
![[asy] import slopefield; real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286; // Label f; // f.p=fontsize(6); xaxis(-1,2); yaxis(-1,2); real f1(real x) { return 3/2 * sin(pi/4 * (x - 1)) + 1/2; } draw(graph(f1,-1,2),MidArrow); draw((0,0)--(1,f1(1)),EndArrow); dot((0,0)); label("$O$",(0,0),NW); label("$\mathbf{r}(t)$",(0.5,f1(1)/2),NNW); [/asy]](http://latex.artofproblemsolving.com/0/5/c/05cb13ea9088a52b8c5589537b367b16a025ccb2.png)
