C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Program to compute basin of attraction of C a Forced Damped Pendulum C using 4th order Runge-Kutta Method C A number of steps using RK4 is performed and the sign C of angular velocity is printed on stdout C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC program fdp_solve implicit none integer P parameter(P=1010000) real*8 T0,TF,X10,X20 integer STEPS,PSIZE real*8 T(P),X1(P),X2(P) real*8 Energy real*8 omega_0,omega,gamma,a_0,omega_02,omega2 common /params/omega_0,omega,gamma,a_0,omega_02,omega2 integer i,Nstart real *8 PI2,PI4,PI parameter(PI2=6.283185307179D0,PI4=2.0D0*PI2,PI=PI2/2.0D0) omega_0 = 1.0D0 omega = 2.0D0 omega_02 = omega_0*omega_0 omega2 = omega *omega gamma = 0.2D0 STEPS = 10000 T0 = 0.0D0 TF = 200.0D0 print *, '# Enter A and no of initial conditions:' read(5,*) a_0, Nstart C The Calculation: PSIZE=P do i = 1, Nstart C Random initial conditions with -PI<theta<PI, -2 PI<dtheta/dt<2 PI X10 = PI2*(rand()-0.5D0) X20 = PI4*(rand()-0.5D0) C X10 = PI *rand() C X20 = PI2*rand() call RK(T,X1,X2,T0,TF,X10,X20,STEPS,PSIZE) if( X2(STEPS) .GT. 0.0D0)then print *,X10,X20,1 else print *,X10,X20,-1 endif enddo end C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C The functions f1,f2(t,x1,x2) provided by the user C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC real*8 function f1(t,x1,x2) implicit none real*8 t,x1,x2 f1=x2 !dx1/dt= v = x2 end real*8 function f2(t,x1,x2) implicit none real*8 omega_0,omega,gamma,a_0,omega_02,omega2 common /params/omega_0,omega,gamma,a_0,omega_02,omega2 real*8 t,x1,x2 f2=-(omega_02+2.0D0*a_0*dcos(omega*t))*dsin(x1)-gamma*x2 end C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C RK(T,X1,X2,T0,TF,X10,X20,STEPS,PSIZE) is the driver C for the Runge-Kutta integration routine RKSTEP C Input: Initial and final times T0,T1 C Initial values at t=T0 X10,X20 C Number of steps of integration STEPS C Size of arrays T,X1,X2 C Output: real arrays T(PSIZE),X1(PSIZE),X2(PSIZE) where C T(1) = T0 X1(1) = X10 X2(1) = X20 C X1(i) = X1(at t=T(i)) X2(i) = X2(at t=T(i)) C T(STEPS+1)=TF C Therefore we must have PSIZE>STEPS C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC subroutine RK(T,X1,X2,T0,TF,X10,X20,STEPS,PSIZE) implicit none integer STEPS,PSIZE real*8 T(PSIZE),X1(PSIZE),X2(PSIZE),T0,TF,X10,X20 real*8 dt real*8 TS,X1S,X2S !values of time and X1,X2 at given step integer i C Some checks: if(STEPS .le. 1 )then print *,'rk: STEPS must be >= 1' stop endif if(STEPS .ge. PSIZE)then print *,'rk: STEPS must be < ',PSIZE stop endif C Initialize variables: dt = (TF-T0)/STEPS T (1) = T0 X1(1) = X10 X2(1) = X20 TS = T0 X1S = X10 X2S = X20 C Make RK steps: The arguments of RKSTEP are replaced with the new ones! do i=2,STEPS+1 call RKSTEP(TS,X1S,X2S,dt) T(i) = TS X1(i) = X1S X2(i) = X2S enddo end C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Subroutine RKSTEP(t,x1,x2,dt) C Runge-Kutta Integration routine of ODE C dx1/dt=f1(t,x1,x2) dx2/dt=f2(t,x1,x2) C User must supply derivative functions: C real function f1(t,x1,x2) C real Function f2(t,x1,x2) C Given initial point (t,x1,x2) the routine advnaces it C by time dt. C Input : Inital time t and function values x1,x2 C Output: Final time t+dt and function values x1,x2 C Careful!: values of t,x1,x2 are overwritten... C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC subroutine RKSTEP(t,x1,x2,dt) implicit none real*8 t,x1,x2,dt real*8 f1,f2 real*8 k11,k12,k13,k14,k21,k22,k23,k24 real*8 h,h2,h6,pi,pi2 parameter(pi =3.14159265358979324D0) parameter(pi2=6.28318530717958648D0) h=dt !h =dt, integration step h2=0.5D0*h !h2=h/2 h6=0.166666666666666666666666D0*h !h6=h/6 k11=f1(t,x1,x2) k21=f2(t,x1,x2) k12=f1(t+h2,x1+h2*k11,x2+h2*k21) k22=f2(t+h2,x1+h2*k11,x2+h2*k21) k13=f1(t+h2,x1+h2*k12,x2+h2*k22) k23=f2(t+h2,x1+h2*k12,x2+h2*k22) k14=f1(t+h ,x1+h *k13,x2+h *k23) k24=f2(t+h ,x1+h *k13,x2+h *k23) t =t+h x1=x1+h6*(k11+2.0D0*(k12+k13)+k14) x2=x2+h6*(k21+2.0D0*(k22+k23)+k24) if( x1 .gt. pi) x1 = x1 - pi2 if( x1 .lt. -pi) x1 = x1 + pi2 end
Robert poop 9:14pmEve are you coming to coffee house my dear? 9:16pmRobert poop yeah mabety 9:16pmEve you should remember that night at the campis household when we were writing poetry I still can’t find that notebook… 9:18pmRobert shit cock. 9:21pmRobert can you see the diffrence ? 9:21pmEve What do you mean? 9:25pmRobert just believe for one second that life is on a beam and one way or the other of every decision of your life will decide the rest of your life each thing you do no matter how simple or small it may seem conducts the symphony of our livves and now that the second is over 9:27pmEve Well, if you think about it, it sort of is, every single choice you make can change your life in one way or another 9:27pmRobert well then why are we here now doing these things? whe could we be other places now doing other things? 9:29pmEve No, because since you are here doing something, there is no other place you should be, because I do believe that everything you do and everything that happens to you happens for a reason, whether it be punishment from you past life or from your ccurrent life, or good karma because of the things you have done. 9:32pmRobert karma is what we are talking about. it has no judgment of right or wrong. it is simlpy the for of consequence, the ever going force that moves though space an time. im comning to the coffee house> ive been coming my entire life. 9:33pmEve yay! I really like people who come to coffee house their entire life I also really like talking to you Robert, you have things to say 9:33pmRobert oh ? poop. fuck facebook. 9:34pmEve Por que? 9:34pmRobert love farmville. porque no? 9:34pmEve Je no ce pas, parle Francais 9:35pmRobert no fuck french just kiddin but i don;t speakcit 9:35pmEve I am really trying to become fluent in French, I want to spend a semester there next year. 9:35pmRobert bonjor 9:36pmEve There’s a start!
fuck you fuck me fuck my tublr and me.