0 20 40

(1)

(3) (3) (2) (2)

(4) (4)

(5) (5) rVM:=0.213:rSR:=0.140:betaNS:=20*3.14/180:rRP:=0.3:rAR:=0.2:

mN:=12.3:mS:=43:mO:=1.2:JNy:=0.3:JOy:=0.0188*mO^2+0.0025*

mO:JSy:=0.87:mNr:=(JNy+JOy)/rVM^2:mSr:=(JSy)/rVM^2:mA:=50:mR:=

62*2:

kNS:=547000:kSRx:=375000:kSRy:=1900000:kARx:=5000000;kARy:=

5000000;kRPx:=770000;kRPy:=1570000;

bNS:=11:bSRx:=1000:bSRy:=1200:bRPx:=1200;bRPy:=1200;bARx:=1200;

bARy:=1200;

FNSa:=200:

omegaNS:=314;

DEQ_sNSr:=((mN+mO)*sin(betaNS)^2+mNr*cos(betaNS)^2)*diff(sNSr (t),t,t)+mNr*diff(xSPr(t),t,t)*cos(betaNS)+(mN+mO)*diff(ySPr(t), t,t)*sin(betaNS)+bNS*diff(sNSr(t),t)+kNS*sNSr(t)=-(-FNSa/2*sin (omegaNS*t)+abs(-FNSa/2*sin(omegaNS*t)))*sin(betaNS);

(2)

(6) (6)

(8) (8) (7) (7)

(9) (9) (5) (5)

(10) (10) DEQ_xSPr:=mNr*diff(sNSr(t),t,t)*cos(betaNS)+(mSr+mNr)*diff(xSPr (t),t,t)+bSRx*rSR^2/rVM^2*(diff(xSPr(t),t)-diff(xRPr(t),t))+

kSRx*rSR^2/rVM^2*(xSPr(t)-xRPr(t))=0;

DEQ_ySPr:=(mN+mO)*diff(sNSr(t),t,t)*sin(betaNS)+(mS+(mN+mO))*

diff(ySPr(t),t,t)+bSRy*(diff(ySPr(t),t)-diff(yRPr(t),t))+kSRy*

(ySPr(t)-yRPr(t))=0;

DEQ_xRPr:=mR*diff(xRPr(t),t,t)+bRPx*rRP^2/rVM^2*diff(xRPr(t),t)+

kRPx*rRP^2/rVM^2*xRPr(t)+bSRx*rSR^2/rVM^2*(diff(xRPr(t),t)-diff (xSPr(t),t))+kSRx*rSR^2/rVM^2*(xRPr(t)-xSPr(t))+bARx*

rAR^2/rVM^2*(diff(xRPr(t),t)-diff(xAPr(t),t))+kARx*rAR^2/rVM^2*

(xRPr(t)-xAPr(t))=0;

DEQ_yRPr:=mR*diff(yRPr(t),t,t)+bRPy*diff(yRPr(t),t)+kRPy*yRPr(t) +bSRy*(diff(yRPr(t),t)-diff(ySPr(t),t))+kSRy*(yRPr(t)-ySPr(t))+

bARy*(diff(yRPr(t),t)-diff(yAPr(t),t))+kARy*(yRPr(t)-yAPr(t))=0;

DEQ_xAPr:=mA*diff(xAPr(t),t,t)+bARx*rAR^2/rVM^2*(diff(xAPr(t),t) -diff(xRPr(t),t))+kARx*rAR^2/rVM^2*(xAPr(t)-xRPr(t))=0;

(3)

(11) (11)

(12) (12) (10) (10)

DEQ_yAPr:=mA*diff(yAPr(t),t,t)+bARy*(diff(yAPr(t),t)-diff(yRPr (t),t))+kARy*(yAPr(t)-yRPr(t))=0;

sysV:={DEQ_sNSr,DEQ_xSPr,DEQ_ySPr,DEQ_xRPr,DEQ_yRPr,DEQ_xAPr, DEQ_yAPr};

(4)

(15) (15) (14) (14) (13) (13) (5) (5)

(12) (12) (10) (10)

IC_sNSr:=sNSr(0)=0,D(sNSr)(0)=0;

IC_xSPr:=xSPr(0)=0,D(xSPr)(0)=0;

IC_ySPr:=ySPr(0)=0,D(ySPr)(0)=0;

IC_xRPr:=xRPr(0)=0,D(xRPr)(0)=0;

IC_yRPr:=yRPr(0)=0,D(yRPr)(0)=0;

IC_xAPr:=xAPr(0)=0,D(xAPr)(0)=0;

IC_yAPr:=yAPr(0)=0,D(yAPr)(0)=0;

ICV:={IC_sNSr,IC_xSPr,IC_ySPr,IC_xRPr,IC_yRPr,IC_xAPr,IC_yAPr};

solnV:=dsolve(sysV union ICV,{sNSr(t),xSPr(t),ySPr(t),xRPr(t), yRPr(t),xAPr(t),yAPr(t)},numeric);

odeplot(solnV,[[t,sNSr(t)+xSPr(t)*cos(betaNS)+ySPr(t)*sin

(betaNS)],[t,xSPr(t)],[t,ySPr(t)]],0..1.5,color=[blue,red,green, brown],view=[1..1.1,-0.0015..0.0015],numpoints=20000,thickness=

2,gridlines=true,axes=boxed,labels = ["t", ""],font=[Camria, roman,14],labelfont=[Cambria,italic,20]);

(5)

(12) (12) (10) (10)

t

0

odeplot(solnV,[[t,kRPy*yRPr(t)+bRPy*diff(yRPr(t),t)],[t,

rRP^2/rVM^2*(kRPx*xRPr(t)+bRPx*diff(xRPr(t),t))]],0..1.5,color=

[blue,red,green],view=[1..1.1,-50..50],numpoints=20000,

thickness=2,gridlines=true,axes=boxed,labels = ["t", ""],font=

[Camria,roman,14],labelfont=[Cambria,italic,20]);

(6)

(5) (5)

(12) (12) (10) (10)

t

0 20 40

odeplot(solnV,[[t,yRPr(t)],[t,xRPr(t)]],0..1.5,color=[blue,red, green],view=[1..1.1,-0.00001..0.00001],numpoints=20000,

thickness=2,gridlines=true,axes=boxed,labels = ["t", ""],font=

[Camria,roman,14],labelfont=[Cambria,italic,20]);

(7)

(12) (12) (10) (10)