Classical Mechanics

Conservative Forces and Energy
1. T=⅟₂mẋ
2. W= ∫F dx =⅟₂ mẋ²(t)-⅟₂mẋ²(t)
3. E= ⅟₂mẋ²+V(x(t))
Stability and Equilibrium
1. E≥V(x) is BOUNDED MOTION
2. E=V(x), ẋ=0, PARTICLE IS STATIONARY
3. EQUILIBRIUM POINT: 0=dv/dx (x)
Second Order Equations
1. If D>0. λ₁, λ₂ exist.
  1. Gen Sol: x(t)= C1e^λ1t + C2e^λ2t
2. If D<0 z1,2 exist as complex conjugate
  1. Gen Sol: x(t)= e^ λt(C1cos(ϴt)+C2sin( ϴt))
3. If D=0, z1=z2
  1. Gen Sol: x(t)= (C1+C2)e^λt
Imulsive Motion
1. Coefficient of restitution, e
  1. e=o, coalesce
  2. 0<e<1, |v1-v2|=e|u1-u2|
  3. e=1, elastic coll. No los in KE
  4. e>1, Super elastic.
2. Linear Momentum
  1. p(t1)-p(t0)= ∫ F dt
  2. p=m. d/dx (r)
3. Momentum is p=mV

Zusammenfassung der Ressource

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