In[]:=
ClearAll["Global`*"]​​​​m=35.25;(*kg*)​​l=5;(*m*)​​b=0.3;(*m*)​​h=0.025;(*m*)​​r=l/2-1.7;(*m*)​​roh=940;(*kg/m^3*)​​my=0.3;​​g=9.81;(*m/s^2*)​​​​(*Haften*)​​​​sol=NDSolve[{phi''[t]==(12*g*(r*Cos[phi[t]]-(h/2)*Sin[phi[t]]))/(l^2+4*h^2+12*r^2),phi[0]==0,phi'[0]==0},phi,{t,0,10}];​​​​FR[phi_,phiPrime_,phiSecond_]:=-(m*h)/2*phiSecond+m*r*phiPrime^2+m*g*Sin[phi]​​FN[phi_,phiPrime_,phiSecond_]:=-m*r*phiSecond-(m*h)/2*phiPrime^2+m*g*Cos[phi]​​​​fnPlot=Plot[FN[phi[t],phi'[t],phi''[t]]/.sol,{t,0,0.5},PlotStyle->Blue,PlotRange->All,AxesLabel->{"t","FN"}];​​frPlot=Plot[FR[phi[t],phi'[t],phi''[t]]/.sol,{t,0,0.5},PlotStyle->Red,PlotRange->All,AxesLabel->{"t","FR"}];​​solPlot=Plot[Evaluate[(phi[t]/.sol)*360/(2*Pi)],{t,0,0.5},PlotStyle->Green,PlotRange->All,AxesLabel->{"t","phi"}];​​{fnPlot,frPlot,solPlot}​​​​tkrit=t/.FindRoot[FR[phi[t],phi'[t],phi''[t]]==my*FN[phi[t],phi'[t],phi''[t]]/.sol,{t,1}]​​FNkrit=FN[phi[tkrit],phi'[tkrit],phi''[tkrit]]/.sol​​FRkrit=FR[phi[tkrit],phi'[tkrit],phi''[tkrit]]/.sol​​phikrit=(phi[tkrit]/.sol)*180/Pi​​phiPrimekrit=phi'[tkrit]/.sol​​​​Manipulate[{FN[phi[t],phi'[t],phi''[t]],FR[phi[t],phi'[t],phi''[t]],phi[t]*360/(2*Pi)}/.sol,{{t,1},0,10,0.001,Appearance->"Labeled"}]​​
Out[]=

,
,

InterpolatingFunction
:Input value {-0.0651544} lies outside the range of data in the interpolating function. Extrapolation will be used.
InterpolatingFunction
:Input value {-0.0651544} lies outside the range of data in the interpolating function. Extrapolation will be used.
InterpolatingFunction
:Input value {-0.0651544} lies outside the range of data in the interpolating function. Extrapolation will be used.
General
:Further output of InterpolatingFunction::dmval will be suppressed during this calculation.
Out[]=
0.330576
Out[]=
{261.081}
Out[]=
{78.3242}
Out[]=
{9.00998}
Out[]=
{0.949434}
Out[]=
​
t
1
FN[phi[1],
′
phi
[1],
′′
phi
[1]],FR[phi[1],
′
phi
[1],
′′
phi
[1]],
180phi[1]
π
/.sol
In[]:=
equ={​​m*(x''[t]-2*phi1'[t]*x'[t]-(r+x[t])*phi1'[t]^2+h/2*phi1''[t])==m*g*Sin[phi1[t]]-FN1[t]*my,​​m(-(r+x[t])*phi1''[t]-h/2*phi1'[t]^2)==-m*g*Cos[phi1[t]]+FN1[t],​​((l^2+h^2)/12+(h^2)/4+(r+x[t])^2)*m*phi1''[t]+(2*m*(r+x[t])*x'[t])*phi1'[t]==m*g*(r+x[t])*Cos[phi1[t]]+m*g*(h/2)*Sin[phi1[t]],​​x[0]==0,x'[0]==0,​​phi1[0]==(phi[tkrit]/.sol),phi1'[0]==(phi'[tkrit]/.sol)​​};​​tkrit​​​​sol2=NDSolve[equ,{x,phi1,FN1},{t,0,2}]​​Plot[Evaluate[tkrit+(FN1[t]/.sol2[[1,3]])],{t,0,0.5}]​​FNZeroTime=(t/.FindRoot[(FN1[t]/.sol2[[1,3]])==0,{t,0.5}])
Out[]=
0.330576
NDSolve
:Some of the functions have zero differential order, so the equations will be solved as a system of differential-algebraic equations.
Out[]=
xInterpolatingFunction
Domain: {{0.,2.}}
Output: scalar
,phi1InterpolatingFunction
Domain: {{0.,2.}}
Output dimensions: {1}
Data not saved. Save now
,FN1InterpolatingFunction
Domain: {{0.,2.}}
Output: scalar

Out[]=
0.1
0.2
0.3
0.4
0.5
250
260
270
280
290
InterpolatingFunction
:Input value {3.69404} lies outside the range of data in the interpolating function. Extrapolation will be used.
InterpolatingFunction
:Input value {-1.36663} lies outside the range of data in the interpolating function. Extrapolation will be used.
InterpolatingFunction
:Input value {6.63808} lies outside the range of data in the interpolating function. Extrapolation will be used.
General
:Further output of InterpolatingFunction::dmval will be suppressed during this calculation.
Out[]=
2.04825
​