第四讲--椅子放稳模型

,“”“”ABCDACoxθACoxDCBA′′′′xBADCOD´C´B´A´ABCDOθθACf(θ)BDg(θ)f(θ)g(θ)≥0f(θ)g(θ)θf(θ)g(θ)θ=0f(θ)0g(θ)=0pACBDf(p/2)=0g(p/2)0f(θ)g(θ)θθf(θ)•g(θ)=0f(0)0g(0)=0f(θ0)=g(θ0)=0.()02fπ=()02gπ0[0,]2πθ∈θf(θ)g(θ)h(θ)=f(θ)–g(θ)h(0)0h(π/2)0.f(θ)g(θ)h(θ)[0π/2]θ0∈[0,π/2],h(θ0)=0f(θ0)=g(θ0)(θ)•g(θ)=0f(θ0)=g(θ0)=0θf(θ)g(θ)ABCDOABCDOA´B´C´D´θABCDf(θ)ABg(θ)CDABCDf(θ)g(θ)θ,θf(θ)•g(θ)=0f(0)0g(0)=0f(π)=0g(π)0θ∈[0π],f(θ0)=g(θ0)=0θ2222(10000)10000(10000)xyzz++−=ABCDAC=8BD=6ABCDABCDxoyA′B′C′D′256R=258R=25284RAC==22251166(0,,1000010000())D±−−ACD0100007625100006111000022⎟⎠⎞⎜⎝⎛−−⎟⎠⎞⎜⎝⎛−=dxoyAoxABCDoABCDRx2+y2=R2OBOCODθ1θ2θ3.0θ1θ2θ32π.)sin,cos(θθRRA′))sin(),cos((11θθθθ++′RRB))sin(),cos((22θθθθ++′RRC))sin(),cos((33θθθθ++′RRDABCD)0,(RA)sin,cos(11θθRRB)sin,cos(22θθRRC)sin,cos(33θθRRDABCDooA’B’C’D’θθ’’’’xoyozz=f(xy)f(xy)θπz=ϕ(θ).(cos,sin)ARRθθ′11(cos(),sin())BRRθθθθ′++22(cos(),sin())CRRθθθθ′++33(cos(),sin())DRRθθθθ′++(cos,sin,())ARRθθϕθ′′222(cos(),sin(),())CRRθθθθϕθθ′′+++111(cos(),sin(),())BRRθθθθϕθθ′′+++333(cos(),sin(),())DRRθθθθϕθθ′′+++[0,2]θπ∈ABCD′′′′′′′′ϕ(θ)2πR0θ1θ2θ30θ1θ2θ32πθ0∈[0,2π],θ=θ0DCBA′′′′′′′′,,,()[]FABACADθ′′′′′′′′′′′′=JJJJJGJJJJJGJJJJJG{}111cos()cos,sin()sin,()()ABRRRRθθθθθθϕθθϕθ′′′′=+−+−+−JJJJJG{}222cos()cos,sin()sin,()()ACRRRRθθθθθθϕθθϕθ′′′′=+−+−+−JJJJJG{}333cos()cos,sin()sin,()()ADRRRRθθθθθθϕθθϕθ′′′′=+−+−+−JJJJJG[]0ABACAD′′′′′′′′′′′′=JJJJJGJJJJJGJJJJJGDCBA′′′′′′′′,,,111222333cos()cossin()sin()()()cos()cossin()sin()()cos()cossin()sin()()RRRRFRRRRRRRRθθθθθθϕθθϕθθθθθθθθϕθθϕθθθθθθθϕθθϕθ+−+−+−=+−+−+−+−+−+−223321sinsinsin()()()Rθθθθϕθθϕθ=−+−⋅+−⎡⎤⎡⎤⎣⎦⎣⎦231132sinsinsin()()()Rθθθθϕθθϕθ+−+−⋅+−⎡⎤⎡⎤⎣⎦⎣⎦212213sinsinsin()()()Rθθθθϕθθϕθ+−+−⋅+−⎡⎤⎡⎤⎣⎦⎣⎦ϕ(θ)2πa2222000()()()()aaadxdxxdxdππππϕθθϕϕϕθθ++===∫∫∫∫210[()()]0dπϕθθϕθθ+−=∫230[()()]0dπϕθθϕθθ+−=∫220[()()]0dπϕθθϕθθ+−=∫20()0Fdπθθ=∫θ0∈[0,2π]2001()()02FFdπθθθπ==∫[]0ABACAD′′′′′′′′′′′′=JJJJJGJJJJJGJJJJJGθ=θ0,,,ABCD′′′′′′′′“”“”ABBAACBA′B′C′