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This system is best analyzed using Lagrangian mechanics. Choose the generalized coordinate to be the angle To explore these problems further, do you need
The legendary Soviet-era book that is a rite of passage for physics competitors. T=12M(23g)=13Mgcap T equals one-half cap M open paren
T=12M(23g)=13Mgcap T equals one-half cap M open paren two-thirds g close paren equals one-third cap M g 4. Advanced Analytical Mechanics: The Double Wire Pendulum A bead of mass Therefore, (Simulated Link)
L=12mR2θ̇2+12mR2ω2sin2θ−mgR(1−cosθ)cap L equals one-half m cap R squared theta dot squared plus one-half m cap R squared omega squared sine squared theta minus m g cap R open paren 1 minus cosine theta close paren
ddt[r+vu(xA−x)]=(−u+vcosθ)+(v2u−vcosθ)=−u+v2u=−u2−v2ud over d t end-fraction open bracket r plus v over u end-fraction open paren x sub cap A minus x close paren close bracket equals open paren negative u plus v cosine theta close paren plus open paren the fraction with numerator v squared and denominator u end-fraction minus v cosine theta close paren equals negative u plus the fraction with numerator v squared and denominator u end-fraction equals negative the fraction with numerator u squared minus v squared and denominator u end-fraction This is a constant! We can integrate this directly from (the time of interception). Therefore,
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