698473
Classical Mechanics
- Conservative Forces and Energy
- T=⅟₂mẋ
- W= ∫F dx =⅟₂ mẋ²(t)-⅟₂mẋ²(t)
- E= ⅟₂mẋ²+V(x(t))
- T=⅟₂mẋ
- Stability and Equilibrium
- E≥V(x) is BOUNDED MOTION
- E=V(x), ẋ=0, PARTICLE IS STATIONARY
- EQUILIBRIUM POINT: 0=dv/dx (x)
- E≥V(x) is BOUNDED MOTION
- Second Order Equations
- If D>0. λ₁, λ₂ exist.
- Gen Sol: x(t)= C1e^λ1t + C2e^λ2t
- Gen Sol: x(t)= C1e^λ1t + C2e^λ2t
- If D<0 z1,2 exist as complex conjugate
- Gen Sol: x(t)= e^ λt(C1cos(ϴt)+C2sin( ϴt))
- Gen Sol: x(t)= e^ λt(C1cos(ϴt)+C2sin( ϴt))
- If D=0, z1=z2
- Gen Sol: x(t)= (C1+C2)e^λt
- Gen Sol: x(t)= (C1+C2)e^λt
- If D>0. λ₁, λ₂ exist.
- Imulsive Motion
- Coefficient of restitution, e
- e=o, coalesce
- 0<e<1, |v1-v2|=e|u1-u2|
- e=1, elastic coll. No los in KE
- e>1, Super elastic.
- e=o, coalesce
- Linear Momentum
- p(t1)-p(t0)= ∫ F dt
- p=m. d/dx (r)
- p(t1)-p(t0)= ∫ F dt
- Momentum is p=mV
- Coefficient of restitution, e
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