v[theta_]:=mgl*Cos[theta]

ppsi[theta_,phidot_,psidot_]:=i3*(psidot+Cos[theta]*phidot)

pphi[theta_,phidot_,psidot_]:=iperp*(Sin[theta])^2*phidot+ppsi[theta,phidot,psidot]*Cos[theta]

veff[theta_,ppsi_,pphi_]:=0.5*(pphi-ppsi*Cos[theta])^2/iperp/(Sin[theta])^2+v[theta]

Assume initially theta-dot equals to zero. Set the constants to some arbitrary numbers

i3=1.5; iperp=1.0; mgl=10.0

{Slider[Dynamic[thin],{0.01,3.14,0.01}],Style[NumberForm[Dynamic[thin],{3,2}]]}

{Slider[Dynamic[psidotin],{0.0,62.83,0.1}],Style[NumberForm[Dynamic[psidotin],{3,2}]]}

{Slider[Dynamic[phidotin],{-31.4,31.4,0.1}],Style[NumberForm[Dynamic[phidotin],{3,2}]]}

Dynamic[pps=ppsi[thin,phidotin,psidotin]]

Dynamic[pph=pphi[thin,phidotin,psidotin]]

Dynamic[eeff=veff[thin,pps,pph]]

phidot[theta_]:=(pph-pps*Cos[theta])/iperp/(Sin[theta])^2

psidot[theta_]:=pps/i3-Cos[theta]*phidot[theta]

{Slider[Dynamic[pr],{0.01,1000,0.1}],Style[NumberForm[Dynamic[pr],{3,2}]]}

Dynamic[Plot[{veff[thet,pps,pph],phidot[thet],psidot[thet],eeff},{thet,0.1,3.0},PlotRange->{-pr,pr}]]

Blue=veff, Orange = phidot, Green = psidot, Red =eeff =  total effective energy