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Of course it is possible for the rigid body to change the axis of rotation itself, for example, cats do it and they always fall on four legs, but it must be done in accordance with the laws of physics. This movement describes the Euler equation of motion and the mechanism of occurrence of the internal moment of force presents this scheme.ribes How this moment of force works during the dzanibekowa effect shows this simulation Here is a change in angular velocities relative to body

My simulations show a lot more of details which you will not see elsewhere, and angular acceleration or moment of force is a completely new approach to this issue

which exactly step? During the mechanics of rotation of the rigid body angular velocity is constant only in three special cases only when it rotates exactly around one of the main axes of the moment of inertia in other cases, the vector is not stable in the body frame and inertial frame. It shows my animation another simulation shows the same There was an error in my Euler patterns, I will try to fix it quickly How to edit a note? correction of Euler's equations Ix(dωx/dt)= (Iy - Iz)ωzωy Iy(dωy/dt)= (Iz - Ix)ωzωx Iz(dωz/dt)= (Ix - Iy)ωxωy

I am interested in the mechanics of rigid body rotation. I entered the subject very deeply, and from my calculations and conclusions it follows that, not everything is exactly that haw it is written in books and few details have hidden in present science . Of course, these are my conclusions and should be verified but no one did not get interested, and physicists are afraid of the subject, like the devil of holy water. I thought I might find people here with whom I could discuss the issue, but because the questions for I am looking answers can not be found in books, they only hear excuses. Unfortunately, the local community is just waiting for easy questions which answers can be found in books, and he has not been interested in searching for answers that have not yet been found. To better introduce you to the topic I prepared simulations showing rigid body rotation based on Poisnot solutions using the ellipsoid concept. Solutions in the sources which I have, it was very chaotically written but I finally managed to understand and sort it. What is matter? During the rotation of the rigid body, the moment of inertia is the most important thing. Each rigid body has three constant moments of inertia which is permanently attached to the solid frame. It means that in the body configuration, the moment of inertia is constant over time. Poinsot presented it in the form of an ellipsoid of inertia in the body configuration. It is interesting that, if we have different main moments of inertia and the body rotates near the middle moment of inertia, comes to the Dzibibekov effect that is, for spontaneous change of the instantaneous axis of rotation. There is a spontaneous change of the angular velocity and changes in the moment of inertia. These changes are not chaotic and predicted that angular velocity vector moves at the intersection of ellipsoid of angular momentum and energy ellipsoid. That's was written but how to understand ellipsoid of angular momentum when the angular momentum is constant over time? My solution is quite simple. Because angular momentum is constans he creates a sphere. L2=Ix2ωx2+ Iy2ωy2+ Iz2ωz2 =Lx2+ Ly2+L2z L=constans Energy is also constant over time and if we used it directly, we would get another sphere. Energy is E=Iω2/2 Angular momentum is L=Iω we can now write energy as E=L2/2I It gives us an ellipsoid 2EI L2=2EIx+2EIy+2EIz Angular momentum is constans in the inertial frame, but is not must be constans relative to the rigid body. This sphere of angular momentum and ellipsoid 2EI are solid relative to the rigid body, so they will rotate with this body in the inertial system. Angular momentum vector is constans in inertial and always it's at the intersection this sphere and the ellipsoid. In rigid body frame this sphere and the ellipsoid they do not move but the angular momentum vector moves along their intersection. Analogously, we can determine the ellipsoid for the angular velocity vector Ω2=2E/Ix+2E/Iy+2E/Iz Ω2=(L/Ix)2+(L/Iy)2+(L/Iz)2 Angular velocity vector moves along their intersection these ellipsoids. Everything is showing my animation. https://youtu.be/p8pwQ39Tx9A The rotation of the rigid body describes Euler's equations Ix(ωx/dt)= (Iy - Iz)ωzωy Iy(ωy/dt)= (Iz - Ix)ωzωx Iz(ωz/dt)= (Ix - Iy)ωxωy I do not know why no one did not see of the relations that resulted from them, ω/dt is definitely the vector of angular accelerations ɛ and Iɛ it is a moment of force. Important, I is the tensor of the moment of inertia, which very complicates calculations but I have pass through it and now I can use it effectively in simulations. There is a superstition that isolated bodies can not have inner moments of forces and internal angular accelerations, but Euler's equations deny it. I have heard a lot of opinion that such a moment of froce would have to be incompatible with the laws of physics, but I examined this moment of force and dont found nothing in it that would contradict any of the laws of Physics. These opinions is result from ignorance, lack of scientific approach and intuitive estimates, dont have nothing to do with the truth. I have proof though it is not yet complete. Conservation of linear angular momentum dL/dt=0 (1) Angular momentum is L= Iω (2) use (1) and (2) d(Iω)/dt= ω(dI/dt) + Iɛ =0 (3) moment of force is M= Iɛ (4) We know that during the rigit body rotation mechanics, the moment of inertia changes over time I showed it in my simulation above . Changing (3) dI/dt=-M/ω (5) we have a pattern for the inner moment of strength M=-ω(dI/dt) (6) we count the derivative with dI/dt M=-ω(dmr^2)/dt (7) the mass is constant, so M=-ωm(2r(dr/dt))=-2ωmrv (8) momentum is p=mv (9) We have now M=-2ωrp (10) Second law of Kepler dA/dt=r(dr/dt)/2= (r x v) /2 = (r x p)/2m (11) S=dA/dt= constans (12) Angular momentum is L = r x p = r x mv (13) Use (11) and (12) r x v = 2S (14) Angular momentum is L=m(r x v)=m2S=2mvr(sina) (15) a - angle between r,v Use (15) to (8) M=-ωL (16) and I found my guess M=-ω x L (17) Using the equation (17) I can effectively simulate the mechanics of rotation. At the end I sending the code in Vpython. How does this moment of force look shows my simulation. https://www.youtube.com/edit?o=U&video_id=8OnWhW1-15s It is only a fragment of my conclusions, there are still some details that still elude me but I'm on the best way to find them. If anyone would like to help or cooperate, I am open to any suggestions. You will find more simulations and details in simulations on my Youtube profile.

Euler's equations. Ix(dωx /dt) + (Iz - Iy)ωzωy = 0 Iy(dωy /dt)+ (Ix - Iz)ωzωx = 0 Iz(dωz /dt)+ (Iy - Ix)ωxωy = 0 Omega must have minimum two no zero elements. If that hapen equations show you dω. Haw this vectors work in nointeria frame show difrent my animation.

My animation works on Euler's equations. In non-inertial frame I finded angular velocity vector and I rotate this frame in interial frame. In this way, I finded the coordinates of the temporary axis of rotation. And I repeat this step a lot time. One step is a very small error but Thousands of steps cause an error to occur. I know how to check those moments force, but I must find time. I'm a very busy person. What improve? This animation shows simple properties this vectors. a=(v1-v0)/dt and F=am. That's all. Sorry but I do not understand the rest.

Hi I would like to present my new simulation rotated rigid ball. Brief introduction to the Dzanibek Effect When I learned to simulate the effect and study the secrets of vector relationships with no problem to finde speed vectors for points. Next step is finde acceleration. It is a=(v1-v0)/dt. To spread this vector I set the angle n of inclination of both vectors and line acceleration it is al=cosn*a. Centrifugal acceleration it is ad=a-al. Now it is easy to determine the force acting on the point. It is F=am. Now I set the angle m between force vector and main axis. Central force is Fc=cosm*F. Remaining component is forces creating a moment of force. Yellow- Velocity Red, lighbrown - acceleration and forces Green - line acceleration Light blue - centrifugal acceleration Pink - Central force Orange – forces give moment of force. My simulation is not perfect and gives errors of the order of 0.01. Sum of moments of forces give result max 0.01 but most likely this is a method error. https://m.salon24.pl/9236008c61194a8bfd80bc37832b8ae7,750,0,0,0.jpg

The mechanics of rigid bodies describe the Euler equations. Ix(dωx /dt) + (Iz - Iy)ωzωy = 0 Iy(dωy /dt)+ (Ix - Iz)ωzωx = 0 Iz(dωz /dt)+ (Iy - Ix)ωxωy = 0 Important is the difference in moments of inertia on the main axes and angular velocity vector components . After easy transformations we have Ixɛx = (Iy - Iz)ωzωy Iyɛy = (Iz - Ix)ωzωx Izɛz = (Ix - Iy)ωxωy Iωω = Iɛ = M - momentum forces Its easily visualize these vectors The problem is that Euler's equations work only in non-inertial systems.

@swansont Thanks for the link, I'm trying to understand this deeper " Is there a question here?" There are many answers in this note but there are still many questions. The main question, how do the centripetal forces work in this effect?

Hi Sorry for my language but I dont speak english very well and probably I have trouble understanding comments. Over a year ago Professor Jadczyk was interested me Dzanibekov's effect. https://www.youtube.com/watch?v=BGRWg4aV2mw Currently I can calculate and simulate a lot. I will use the equations because they are a universal language and they are understandable to all science on over the world. Vector product. a x b = c Perpendicular axis i ┴ j ┴ k Proportions of vectors ck=ai*bj ai=ck/bj bj=ck/ai The inverse of the vector. a(ax,ay,az)=√(ax2+ay2+az2) 1/a=a/a2=(ax/a2, ay/a2, az/a2) Example d (1,1,1) 1/d (1/3, 1/3, 1/3) e (1,1,0) 1/e (1/2, 1/2, 0) f (1,0,0) 1/f (1,0,0) Easy vector product equations. c = a x b a = 1/b x c b = c x 1/a Vector product equations for velocity, angular velocity and position. These equations are correct only for a free point. v = ω x r = 1/s * m ω = 1/r x v = 1/m * m/s r = v x 1/ω = m/s * s In rigid body rotation usually Angular velocity is not stable. https://youtu.be/CAVXGDMbquk How to calculate temporary angular velocity for rigid body rotation? Rigid body elements m1x`(√2, √2, 0); v1(0,0,-2) m2x`(-√2, -√2, 0); v2(0,0,2) m3y`(-√2, √2, 0); v3(0,0,-2) m4y`(√2, -√2, 0); v4(0,0,2) m1,m2 is x` main axis. m3,m4 is y` main axis. The center of mas is the center of the coordinate system. We calculate angular velocity for main axis ωx`=(-√2/2, √2/2, 0) ωy`=(-√2/2, -√2/2, 0) These are components temporary angular velocity for rigid body rotation Ω = ωx` + ωy` =(√2, 0, 0) https://m.salon24.pl/051c2bf7373b20e081ac0f25ababa170,750,0,0,0.jpg How to calculate velocity? Property vector product: a x b = c ---> c=absinα If Ω (x,0,0) and r (x,y,0) this give ry┴Ω i rx║Ω v = Ω x ry Angular momentum for the free point L = r x p Angular momentum for rigid body show that equations using tensor moment of inertia. Lx= ωxΣmn(rn2-xn2) + ωyΣmnxnyn + ωzΣmnxnzn Ly= ωxΣmnynxn + ωyΣmn(rn2-yn2) + ωzΣmnynzn Lz= ωxΣmnznxn + ωyΣmnznyn + ωzΣmn(rn2-zn2) r is the position point to the center of mass. Easier equations using moment of inertia for main axis Ix=mxr2 + m-xr2; Iy=myr2=m-yr2 Lx = (r1 x p1)x + (r2 x p2)-x Ly = (r3 x p3)y + (r4 x p4)-y Lz = (r5 x p5)z + (r6 x p6)-z L = Lx + Ly + Lz Centripetal acceleration ad for point. ad=rω2 --> rω=v ad=v2/r --> v/r=ω ad=ωv ad║-r Vector product equations for centripetal acceleration ad = ω x v ω = 1/v x ad v =ad x 1/ω Equations temporary angular velocity for rigid body rotation Ω=ωx`+ωy`+ωz`=(1/v x ad)x` + (1/v x ad)y` + (1/v x ad)z` Centripetal forces for point in rigid body rotation, three possibilities. First version F=am ω = 1/v x ad ω = 1/mv x mad ω = 1/p x Fd Fd = ω x p p = Fd x 1/ω Second version Ω = (x, 0, 0) r = rx +ry = r┴ + r║ Fd=mω2 ry Third version Ω = (x, 0, 0) r = rx +ry = r┴ + r║ Fd=mω2 r Fd=m(1/ry x v)2 r Everything shows my animation https://youtu.be/oz1uw9x13kA Another animation shows the angular acceleration vector for the effect https://youtu.be/exwM5bTuO6Q https://youtu.be/v2kwwzLA3aM Another animation shows the vectors in no inertial frame https://youtu.be/LZ9YwG9cVBE code for the first simulation Vpython. from visual import * mx=0.5 #masy x`,y` my=1. x1=1 #pozycja m1,m2 na osi x` y1=0 z1=0 x2=0 #pozycja m3,m4 na osi y` y2=1 z2=0 r=vector(x1,y1,z1) #promien R=mag(r) #print R W=vector(0.9,0,0) #omega v1=W.x*y1 #predkosci v2=W.x*-y1 v3=W.x*y2 v4=W.x*-y2 p1=mx*v1 #ped p2=mx*v2 p3=my*v3 p4=my*v4 ax=(v1*v1) #przyspieszenia a=(v^2)/r; r=1 ay=(v3*v3) #print "v",v1,v2,v3,v4 TIxx=(2*mx*((y1*y1)+(z1*z1)))+(2*my*((y2*y2)+(z2*z2))) #mx1 i mx2 --> 2*mx TIyy=(2*mx*((x1*x1)+(z1*z1)))+(2*my*((x2*x2)+(z2*z2))) #elementy tensora TIzz=(2*mx*((x1*x1)+(y1*y1)))+(2*my*((x2*x2)+(y2*y2))) TIxy=(2*mx*x1*y1)+(2*my*x2*y2) TIxz=(2*mx*x1*z1)+(2*my*x2*z2) TIyx=(2*mx*y1*x1)+(2*my*y2*x2) TIyz=(2*mx*y1*z1)+(2*my*y2*z2) TIzx=(2*mx*z1*x1)+(2*my*z2*x2) TIzy=(2*mx*z1*y1)+(2*my*z2*y2) Fdx=mx*W.x*W.x*y1 #sily dosrodkowe na osiach glownych z Fd=mW^2ry Fdy=my*W.x*W.x*y2 #print "F", Fd1,Fd2 Fdax=mx*ax #sily dosrodkowe na osiach glownych z F=ma Fday=my*ay #L=vector((W.x*TIxx-W.y*TIxy-W.z*TIxz),(-W.x*TIyx+W.y*TIyy-W.z*TIyz),(-W.x*TIzx-W.y*TIzy+W.z*TIzz)) #print "W",W omega=arrow(axis=vector(W.x,W.y,0), color= color.blue, shaftwidth=0.05) #omega startowa #kret=arrow(axis=vector(0,0,0), color= color.red, shaftwidth=0.04) kret2=arrow(axis=vector(0,0,0),color=vector(1,0.4,0.4), shaftwidth=0.04) #kret2x=arrow(axis=vector(0,0,0),color=vector(1,1,0.3), shaftwidth=0.04) #kret2y=arrow(axis=vector(0,0,0),color=vector(1,1,0.3), shaftwidth=0.04) dv1=arrow(axis=vector(0,0,0), color=vector(0.3,0.6,0), shaftwidth=0.05) #przyspieszenie punktow dv2=arrow(axis=vector(0,0,0), color=vector(0.3,0.6,0), shaftwidth=0.05) dv3=arrow(axis=vector(0,0,0), color=vector(0.3,0.6,0), shaftwidth=0.05) dv4=arrow(axis=vector(0,0,0), color=vector(0.3,0.6,0), shaftwidth=0.05) dvg=arrow(pos=vector(0,1,0),axis=vector(0,0,0), color=vector(0.6,0.6,0), shaftwidth=0.05) dvd=arrow(pos=vector(0,-1,0),axis=vector(0,0,0), color=vector(0.6,0.6,0), shaftwidth=0.05) #omegax=arrow(axis=vector(0,0,0), color= vector(0,0,0.01), shaftwidth=0.02) #omegay=arrow(axis=vector(1,0,0), color= vector(0,0,0.01), shaftwidth=0.02) masa1x=sphere(pos=vector(x1,y1,0),radius=0.05) #bryla sztywna masa2x=sphere(pos=vector(-x1,-y1,0),radius=0.05) masa1y=sphere(pos=vector(x2,y2,0),radius=0.05) masa2y=sphere(pos=vector(-x2,-y2,0),radius=0.05) promien1=arrow(pos=masa2x.pos, axis=masa1x.pos-masa2x.pos, color= color.yellow, shaftwidth=0.005) promien2=arrow(pos=masa2y.pos, axis=masa1y.pos-masa2y.pos, color= color.yellow, shaftwidth=0.005) vm1x=arrow(pos=masa1x.pos, axis=vector(0,0,v1), shaftwidth=0.01) #wektory predkosci punktow vm2x=arrow(pos=masa2x.pos, axis=vector(0,0,v2), color=color.green, shaftwidth=0.01) vm1y=arrow(pos=masa1y.pos, axis=vector(0,0,v3), color=color.green, shaftwidth=0.01) vm2y=arrow(pos=masa2y.pos, axis=vector(0,0,v4), color=color.green, shaftwidth=0.01) #orbita1=ring(pos=vector(x1,0,0), axis=vector(1,0,0), radius=y1, thickness=0.01) #orbita os=arrow(pos=vector(-2,0,0), axis=vector(4,0,0),color=vector(0.3,0.3,0.3),shaftwidth=0.005) #os obrotu sila1=arrow(pos=masa1x.pos,axis=-vector(x1,y1,0)*Fdx, color= vector(1,1,0), shaftwidth=0.05) #wektory sil dosrodkowych punktow sila2=arrow(pos=masa1x.pos,axis=-vector(-x1,-y1,0)*Fdx, color= vector(1,1,0), shaftwidth=0.05) sila3=arrow(pos=masa1y.pos,axis=-vector(x2,y2,0)*Fdy, color= vector(1,1,0), shaftwidth=0.05) sila4=arrow(pos=masa1y.pos,axis=-vector(-x2,-y2,0)*Fdy, color= vector(1,1,0), shaftwidth=0.05) sumasilag=arrow(color= vector(0.8,0.5,0), shaftwidth=0.05) #suma sil dosrodkowych gora z Fd=mW^2ry sumasilad=arrow(color= vector(0.8,0.5,0), shaftwidth=0.05) #suma sil dosrodkowych dol z Fd=mW^2ry #sila1a=arrow(pos=masa1x.pos,axis=-vector(x1,y1,0)*Fdax, color= vector(1,1,0.5), shaftwidth=0.05) #wektory sil dosrodkowych punktow #sila2a=arrow(pos=masa1x.pos,axis=-vector(x1,y1,0)*Fdax, color= vector(1,1,0.5), shaftwidth=0.05) #wektory sil dosrodkowych punktow #sila3a=arrow(pos=masa1x.pos,axis=-vector(x1,y1,0)*Fday, color= vector(1,1,0.5), shaftwidth=0.05) #wektory sil dosrodkowych punktow #sila4a=arrow(pos=masa1x.pos,axis=-vector(x1,y1,0)*Fday, color= vector(1,1,0.5), shaftwidth=0.05) #wektory sil dosrodkowych punktow #sumasilga=arrow(color= vector(0.8,0.5,0), shaftwidth=0.05) #suma sil dosrodkowych dol F=am #sumasilda=arrow(color= vector(0.8,0.5,0), shaftwidth=0.05) #suma sil dosrodkowych dol F=am #sumaF=arrow(axis=-vector(0,Fd1+Fd2,0), color= vector(1,0.5,0), shaftwidth=0.03) t=0 while t<20: rate(3) # print t,L # print TIxx-TIxy-TIxz,-TIyx+TIyy-TIyz,-TIzx-TIzy+TIzz # print TIxx,TIxy,TIxz," I ",TIyx,TIyy,TIyz," I ",TIzx,TIzy,TIzz x1=x1-0.1 #nowe pozycje punktow y1=sqrt(1-(x1*x1)) y2=y2-0.1 x2=-sqrt(1-(y2*y2)) v1=W.x*y1 # v = W x ry v2=W.x*-y1 v3=W.x*y2 v4=W.x*-y2 ov1=1/v1 #1/v ov2=1/v2 ov3=1/v3 ov4=1/v4 # print t,v1*ov1 r1=vector(x1,y1,0) #promienie r2=vector(-x1,-y1,0) r3=vector(x2,y2,0) r4=vector(-x1,-y1,0) # print mag(r1),mag(r2),mag(r3),mag(r4) p1=mx*v1 #ped p2=mx*v2 p3=my*v3 p4=my*v4 op1=1/p1 #1/p op2=1/p2 op3=1/p3 op4=1/p4 # print "v",v1,v2,v3,v4, "p",p1,p2,p3,p4 wx=vector(y1*v1,-(x1*v1),0) # wx` = r x v12; r=1 wy=vector(y2*v3,-(x2*v3),0) # wy` = r x v34; r=1 Wk=wx+wy # omega koncowa Wk=wx`+wy` # print t, "Ws=", W, "Wk=", Wk a1=(v1*v1)/mag(r1) #przyspieszenia a=(v^2)/r; r=1 a2=(v2*v2)/mag(r2) a3=(v3*v3)/mag(r3) a4=(v4*v4)/mag(r4) a1v=vector(x1,y1,0)*-a1 #wektory przyspieszen a2v=vector(-x1,-y1,0)*-a2 a3v=vector(x2,y2,0)*-a3 a4v=vector(-x2,-y2,0)*-a4 # a1r=-r1*(v1*v1) # f1am=a1*mx # print t, f1am # print t,a1,a2 if t<10: #suma par przyspieszen dosrodkowych gora, dol z Fd=mW^2ry adg=a1v+a3v add=a2v+a4v else: adg=a1v+a4v add=a2v+a3v Wax=vector(-ov1*a1v.y,ov1*a1v.x,0) # w = 1/v x a Way=vector(-ov3*a3v.y,ov3*a3v.x,0) Wa=Wax+Way #W=wx`+wy` # print t, Wa # r1=sqrt((x1*x1)+(y1*y1)) TIxx=(2*mx*((y1*y1)+(z1*z1)))+(2*my*((y2*y2)+(z2*z2))) #mx1 i mx2 --> 2*mx TIyy=(2*mx*((x1*x1)+(z1*z1)))+(2*my*((x2*x2)+(z2*z2))) TIzz=(2*mx*((x1*x1)+(y1*y1)))+(2*my*((x2*x2)+(y2*y2))) TIxy=(2*mx*x1*y1)+(2*my*x2*y2) TIxz=(2*mx*x1*z1)+(2*my*x2*z2) TIyx=(2*mx*y1*x1)+(2*my*y2*x2) TIyz=(2*mx*y1*z1)+(2*my*y2*z2) TIzx=(2*mx*z1*x1)+(2*my*z2*x2) TIzy=(2*mx*z1*y1)+(2*my*z2*y2) L=vector((W.x*TIxx-W.y*TIxy-W.z*TIxz),(-W.x*TIyx+W.y*TIyy-W.z*TIyz),(-W.x*TIzx-W.y*TIzy+W.z*TIzz)) if y1<0: #wartosc sily dosrodkowe Fd=mW^2ry Fdx=mx*W.x*W.x*y1 else: Fdx=-mx*W.x*W.x*y1 if y2<0: Fdy=my*W.x*W.x*y2 else: Fdy=-my*W.x*W.x*y2 # print t, Fdy, x2,y2 Lpr1=vector(y1*p1,-x1*p1,0) # L = r x p Lpr2=vector(-y1*p2,x1*p2,0) Lpr3=vector(y2*p3,-x2*p3,0) Lpr4=vector(-y2*p4,x2*p4,0) Lprx=Lpr1+Lpr2 Lpry=Lpr3+Lpr4 Lpr=Lprx+Lpry #suma kretow # print t, L-Lpr Fd1=vector(x1,y1,0)*Fdx #wektory sil dosrodkowch z Fd=mW^2ry Fd2=vector(-x1,-y1,0)*Fdx Fd3=vector(x2,y2,0)*Fdy Fd4=vector(-x2,-y2,0)*Fdy if t<10: #suma par sil dosrodkowych gora, dol z Fd=mW^2ry Fdg=Fd1+Fd3 Fdd=Fd2+Fd4 else: Fdg=Fd1+Fd4 Fdd=Fd2+Fd3 Fd1a=a1v*mx #F=am Fd2a=a2v*mx Fd3a=a3v*my Fd4a=a4v*my WFpx=vector(-op1*Fd1a.y,op1*Fd1a.x,0) #w = (1/p) x F WFpy=vector(-op3*Fd3a.y,op3*Fd3a.x,0) WFp=WFpx+WFpy # print t, WFp, W if t<10: #suma par sil dosrodkowych gora, dol z F=ma Fdag=Fd1a+Fd3a Fdad=Fd2a+Fd4a else: Fdag=Fd1a+Fd4a Fdad=Fd2a+Fd3a print t,Fdag, Fdad # kret.axis=vector(L.x,L.y,L.z+0.01) kret2.axis=vector(Lpr.x,Lpr.y,Lpr.z+0.01) # kret2x.axis=vector(Lprx.x,Lprx.y,Lprx.z+0.01) # kret2y.axis=vector(Lpry.x,Lpry.y,Lpry.z+0.01) masa1x.pos=vector(x1,y1,0) masa2x.pos=vector(-x1,-y1,0) masa1y.pos=vector(x2,y2,0) masa2y.pos=vector(-x2,-y2,0) promien1.pos=masa2x.pos promien1.axis=masa1x.pos-masa2x.pos promien2.pos=masa2y.pos promien2.axis=masa1y.pos-masa2y.pos vm1x.pos=masa1x.pos vm1x.axis=vector(0,0,v1) vm2x.pos=masa2x.pos vm2x.axis=vector(0,0,v2) vm1y.pos=masa1y.pos vm1y.axis=vector(0,0,v3) vm2y.pos=masa2y.pos vm2y.axis=vector(0,0,v4) # orbita1.pos=vector(x1,0,0) # orbita1.radius=y1 # omegax.axis=wx # omegay.axis=wy # dv1.pos=vector(x1,y1,0) # dv1.axis=vector(a1v.x,a1v.y,a1v.z) # dv2.pos=vector(-x1,-y1,0) # dv2.axis=vector(a2v.x,a2v.y,a2v.z) # dv3.pos=vector(x2,y2,0) # dv3.axis=vector(a3v.x,a3v.y,a3v.z) # dv4.pos=vector(-x2,-y2,0) # dv4.axis=vector(a4v.x,a4v.y,a4v.z) # dvg.axis=vector(adg.x,adg.y,adg.z) # dvd.axis=vector(add.x,add.y,add.z) sila1.pos=vector(x1,y1,0) # sila1.axis=vector(0,-mag(Fd1),0) sila1.axis=vector(Fd1.x,Fd1.y,Fd1.z) sila2.pos=vector(-x1,-y1,0) # sila2.axis=vector(0,mag(Fd2),0) sila2.axis=vector(Fd2.x,Fd2.y,Fd2.z) sila3.pos=vector(x2,y2,0) sila3.axis=vector(Fd3.x,Fd3.y,Fd3.z) sila4.pos=vector(-x2,-y2,0) sila4.axis=vector(Fd4.x,Fd4.y,Fd4.z) # if t<10: # sila3.axis=vector(0,-mag(Fd3),0) # sila4.axis=vector(0,mag(Fd4),0) # else: # sila3.axis=vector(0,mag(Fd3),0) # sila4.axis=vector(0,-mag(Fd4),0) sumasilag.axis=vector(Fdg.x,Fdg.y,Fdg.z) sumasilad.axis=vector(Fdd.x,Fdd.y,Fdd.z) # sila1a.pos=vector(x1,y1,0) # sila1a.axis=vector(Fd1a.x,Fd1a.y,Fd1a.z) # sila2a.pos=vector(-x1,-y1,0) # sila2a.axis=vector(Fd2a.x,Fd2a.y,Fd2a.z) # sila3a.pos=vector(x2,y2,0) # sila3a.axis=vector(Fd3a.x,Fd3a.y,Fd3a.z) # sila4a.pos=vector(-x2,-y2,0) # sila4a.axis=vector(Fd4a.x,Fd4a.y,Fd4a.z) # sumasilga.axis=vector(Fdag.x,Fdag.y,Fdag.z) # sumasilda.axis=vector(Fdad.x,Fdad.y,Fdad.z) # sumaF.axis=sila1.axis+sila2.axis # LxF=sumaF.axis.x*L.x+sumaF.axis.y*L.y+sumaF.axis.z*L.z # print t,"L x F",LxF t=t+1