3.2 Аналитическое решение модели.

квадратурах. kl

QmVmXX С4

avVv

VmavVv О і ? о о і ???

Tg(0 =

\2CmGmk3 2кЗ

2 GgCgVg

2VgGgk3^ Vg Cg Qg kl 2QnQm VS % k!av ^ +2ltnCm2 Gm2 VgCgGgklX\k3-2VmCm2 Gm2 VgCgGg к lav Vv + av2 Vv2Vg2 Cg2 Gg2-2 IfaavVv VgCgGg Cm Gm2X\k3 +2J^av2 V? VgCgGgOnGm + Vm2 Cm2 GmAX\2 k32 + 2Vm Cm2GrnX\ k3 avVv + Vm Cm2 On? av2 V?

-4VmCmGmЈVgCgGgavV*Xk3) f(2CmGmVgGgk3) V \ /QfJ a " j \CmGmVgCgGgkl + avVvVgCgGg + VmCmGm Hk3

+ VmCm GmavV» + {Cm Gm2 Vg2 Cg2 Gg2 kl2-2CmGmV2 Cg GgkUvVv + 2VmCm Gm2 VgCgGgklX\k3 -2VmCm Gm2VgCgGgkiavVv+av2tt2yg2Cg2 Gg2-2tfnavftVgCgGgQnGm2\lk3+2 U(2VmCmGm

+ m2Qn2GrnAX\2k32+2Vm2Cm2 Gm3 X\k3avVv + Vm2 Cm2 Gm2 a2V? -AVmCmGn?VgCgGgavlhXk3) VgCgGg))

k!

avlh

GmVmX 1 G

VmavVv 0 1 1 1 J 0 0 J 0 2 GgCgVg

\2CmGmk3 2 k3 +2faCm2Gm3VgCgGgklXlk3-2VmCm2Gm2VgCgGgkIavft + av2 V?VgCgGg-2VmavV»VgCgGgCmGm2X\k3

+2ma?V?VgCgGgQnGm + Vm2 Cm GmAX\2k32+ 2Vm Cm Gm3\lk3avK> + Vm2 Cm2 Gm2a2 V?

//

\2)

-AVmCmGm2 VgCgGgavV»\k3) /(2 On Gm VgGgk3) V \ * 'Cg

/ J a ~ j -Cm Gm VgCgGgkl-av Vv VgCgGg-VmCmGm X1 k3

-VmCmGmavft + {Cm2 Gm Vg Cg Gg kJ2-2CmGmVg Cg Gg k!avfo+2VmCm2 Gm2 VgCgGgklX\k3

CgGgVm))

Vm Cm (h?X\ k3- C3e'

-Cm Gm Vg Cg Gg kl - av Vv Vg Cg Gg - Vm Cm GmXI kl - Vm On Gmavlfr+(

Cm2 Gm2 Vg Cg Ggkl2-2Cm Gm V2 Cg Gg2klw Vv+7mCmGn? VgCgGgklX 1 H-2 Vm Cm2 Gm2 Vg CgGgkl av ЇЛ +qv2V? Vg Cg G2-2VmavV>>VgCgGgCmGm Xi kl + 2 Vmav2 V? VgCg Gg Cm Gm + Ш2 Qn2Gm2Xl2k32

lYl 1/(2 Cm GmVg CgGgVm))

On G

-(-2 Vf? Cm Gm3 XI k3 av + Vm2 On Gm2 a2V?-A VmCm Gm2 Vg Cg Gg av V»\k3) Ggkl + J3t

k-On Gm VgCg Gg И-avVv Vg CgGg- Vm On Gm2 XI k3 - Vm Cm Gm av ft-i-(Cm2 Gm2 Vg Cg Gg2ki2 -2CmGmVg2 Cg2 Gg2 Uav И-+2 Vm Cm Gm3 VgCg Ggkl Xlk3-2VmGn2 Gm2 Vg Cg Ggklav V»+a2 V? Vg Cg Gg -2VhwVi>VgCgGgQ7iGm2X\k3 + 2Mnav2 V? VgCg Gg Cm Gm + Vn? Cm2 GmA\\2k32 +2 Vm On2 Gm3Jdk3avVv

ПЇ U(2CmGmVg

+ Их2 On2 Gm4 XI2 k32+2 Ifa2 Ся? Gro^ J.1 k3av Vt + Vm2 On2 Gm2av2 Vit2-4VmCm Gm2 VgCgGgavVvXk3) ) CgGgVm)}

ki a

-X(f) = .C2+_Ge

k3

-CmGmVgCgGgkl-avVvVgCgGg-VmCmGn?X\ k3-VmCmGmavVv + ( Ch2Gm2Vg2Cg2Gg2kl2-2CmGmVg2Cg2Gg2klavto + 2VmCm2Gm3VgC^

+av2 fo2Vg2Cg2Gg2-2lfacvVi?VgCgGgQ7iGm2\ik3 + 2faav2ft2VgCgGgCmGm + m^ U{2CmGmVgCgGgVm))

+ at

+2Vm Gm3 X\k3avVv + m2 On2 Gm qv2 V? -АШСт } CmGmVgCgGgkI+avVi>ygCgGg+lfaCmGm2Xlk3 + lfaCmGmQvVi>+(^

+2 Vm Cm Gm3 Vg Cg Ggkl XI k3 - 2 Vm Cm Gm Vg Cg Ggkl cv Vi> + a? Vv2Vg2Cg2Gg2-2VmavVvVgCgGgCmGm2Xlk3 +2Vmw2V>2VgCgGgCmGm + Vm2 Cm2 GmAX\2k32+2Ш2 Cm2 Gm3 X\k3a*V* + Vm CmGma?V?

lYl -m<&GmX\k3-VmQnGmwV>+(Cm Gm2Vg2 Cg2Gg2kl2-2CmGmVg2Cg2Gg2kIavV*+2VmCm2 Gm3 VgCg Ggkl X\k3 -2VmCm Gm2 VgCg Ggkl avV»+av2 V?Vg Cg Gg Vv VgCgGg On GmX\k3^2Vm av2 Vv2VgCgGgCmGm

іуі l/(2CmGmVg

+ 2 Cm GmAX\2k32+2Vn?CmGmX\k3avV* + Vm On2 Gm2 a2V?-AtfnCmGm2 VgCgGg avV>Xk3) lf(2CmGmVgCgGgVm),

Pfo Cm Gmav 1>\>- C&t

+ Ил2 Cm2 Gm2av2 Vv2-4VmCm От2 VgCgGgavl>\>Xk3) ChGmVgCgGgkl + avVvVgCgGg+lfaQnGm2Xlk3 + lfaCmGmavft + (Qn2 Gm2Vg2Cg2Gg2kl2-2CmGmVg2 Cg GgklavVv +2VmCm2 Gm3 VgCgGgklX\k3-2VmOn GmVgCgGgklavVv+a2 V?Vg Cg2 Gg2-2Vm avVv VgCgGg Cm Gn? X\k3 + 2Vmav2V?VgCgGgCmGm^Vm2Cm Gm4 X\2 k32 +2 Vm2 Cm2 Gm3 XI k3 av ft + Vm CmGma?V? U{2Vm Cm Gm VgCgGg),

-4 Vm Cm Grn VgCg Ggav ftxH)

Vm On Gm XIW - C*e

\CmGmVgCgGgkl + avVv VgCgGg + 1fotQn Gm2X\ кЗ + Vm Оя Gfacv ft+(Gn2 Gm2 Vg Cg Ggk\^-7Cm Gm Vg Cg Gg2 klavVt+2 Vm On2 Gm3 VgCgGgklXl k3 -2VmCm2Gm2VgCgGgkIavVv+av2 V? Vg Cg Gg - 2 VmavVv VgCgGg Cm Gm2 XL кЗ+2йи й2 V? VgCgGg Cm Gm lt{7VmCmGm

+ lfa2Qn2GmAXl2k32 + 2Vm2Cm2 Gm2 M k3 av W + Ifa2 Cm2 Gm2 av2ft2-4VmCmGm2VgCgGgavV)>\k3) VgCgGg).

{.- {Cm Gm Vg Cg Ggkl + av ft Vg Cg Gg + Vm Cm Gm2 M k3 + Vm Cm Gtoavft+(

CmGmVgCgGgkl+JXt Cm2 Gm2Vf?Cg2 Gg2kl2-2Qn Gm Vg Cg2Gg2ki av ft +2 Jfa Cm2 Gm2 VgCgGgk! Xlk3-2Vm On2 Gm2 VgCgGgklsvVv +av2 Vr2Vg2Cg2Gg2-2VmavVvVgCgGgCmGm2Xik3+2Vmav2 ft2 Vg Cg Gg On Gm + Vm Cm GmX\2k32 \I(2VmCmGmVgCgGg).

IfaQnGmav

+2Ш2On2Gm2X\k3avft> + Wn2Qn2Gm a2ft2 - ОлGm2VgCgGgavVvXk3)

// t, ^t, 2 . „ V^-Оя GmVg CgGgkl-avV* VgCgGg-Vm Cfo Gn?X\k3-VmGmGmw ft + (.

<&2+av2V?VgCgG^-2VmavV*VgCgGgOn(to2X\k3 + 2Mav2V?VgCgGg^ Cm GmAX\2k32

t

U{2CmGmVgCgGgVm),

XVmCmGm

+2 Vn? Cm2 Gm2Uk3avVt + fa2Cm2Gm2av2Vv2-4mCmGm2VgCgGgavVvXk3) кЗ-2 С/с

{Cm Gm Vg Cg GgU+av ft Vg CgGg + Vm Cm GmXX k3 + Vm Cm Gmav ft +{Cm2 Gm2 Vg2 Cg2 Ggkl2 ?2QnGmVg2Cg2Gg2klavVv^2mQn2Gm2VgCgGgklX[k3-2l^Cm2Gm2VgCgGgklavV\> + av2V»2yg2 Cg2 Gg2 -2tfawVvVgCgGgQnGm2Xlk3+2Vmav2Vv2VgCgGgQnGm + lfa2^ і

+ ї^та2 Ол2 Єт4гі2 і:32 + 2 Ил2 Ої2 Gra3 XI jtJ cv ^ + №ї2 On2 Gm2 tjv2 г^2 - 4 ї^з Ол Gm2 rg Cg Ggcv Z^ X jtJ) Jl/(2VmCmGm

4 CZ GS) (y2 Q2 Q2 kl2_2CmGm Vg2 Cg2 Gg2 klavVv+2VmCm2 Gm3 Vg Cg Gg кIM k3 -2VmCm2 Gm2 VgCg Ggkl avft+av2 V? Vg2 Cg2 Gg-2 Vmav V* VgCg GgCm Gm2X\ И+2 Vmav2 V?VgCgGgCmGm

+ ^ХГ + Ол^ cv^ ^ - 4 Иэт Оя Cg Gg av Л H) '

Cm Gm Vg Cg Gg kl+av Vv Vg Cg Gg+Vm Cm Gm'2 Xi k3 + Vm Cm GmwVv^<^2 GmVg Cg Ggkl2-2CmGmVg Cg GgklavVv +2 Ш Cm Gm3Vg Cg Ggkl Xi k3-2 Vm Cm2 Gm Vg Cg Ggkl av Vi> +av2 ft2 Vg2 Cg2 Gg2 - 2 Phi av ft Vg Cg Gg On Gm2 XI k3 +2VmQ2V?VgCgGgCmGm\Vm Cm GmAX\2k32 +2Vm Cm2 Gm3 Wk3civV» + Vm2 Cm2 Gm2 a2V? I*

.2

l/(2VmCmGmVgCgGg).

XVmCmGm k3+ C3t

+ Vm2Cm2 Gmav2 V?-AVmCmGm2 VgCgGgavV»Xk3) -CrnGrnVgCgGgkl-avVvVgCgGg-m<^Gm\\k3-manGmMVv+^

-ICmGmVg Cg GgklavVv^2VmCm2 Gm VgCgGgklX\k3-2VmOr? Gm2VgCgGgklavV»+av2V?VgCgGg -2VmavlfrVgCgGgCmGn?X\k3+2Vmav2 V? VgCgGgCmGm + Vn2 Cm2 GmAXl2 кЗ2+ 2ЇЇП2 Cm2 Gm3Xik3avW

1

l/(2CmGmVgCgGgVm))

\Vm Cm Gm a2 V? -AVmCmGm2VgCgGgavlfrXk3) )

avVvVgCgGg-_C3t

-CmGmVgCgGgkl-avV^VgCgGg'rnCmGm2Xlk3-VmCmGmavVv+{Cm2Gm2V

-2CmGmVg2Cg2Gg2klavVv+2mCm2Gm3VgCgGgklX\k3-2^Cm2Gm2VgCgGgM V^VgCgGg

-2VmavVvVgCgGgCmGmX\k3+2Vmav2 V?VgCgGgCmGm + Vm2Cm2GmAXl2k32 + 2Vm2Cm2Gm3Xlk3avft (Cm Gm2Vg2Cg2Gg2kl2

+ Vm2 On2 Gm2 av2 V? -AVmCmGrn2 VgCgGgavfoXk3) }U(2CmGmVg CgGgVm), -2CmGmV^ Cg GgklavV»+2VmCm2 GmVgCgGgklXW-2VmCm2 Gm2 VgCg Ggklav V^+av2 V?VgCgGg -2VmavV>VgCgGgCmGmX\k3+2mav2 V? VgCgGgCmGm + Vm Cm2 GmAX\2k32+2Vm2 Cm Gm Xlk3avV* .GnGmVgCgGgkl + avVvVgCgGg + WnCmGm 11И

(ї)

+ Ип2 Cm Gm2 av2 V?-AVmCmGm2 VgCgGgavV»Xk3) +_Cfe + VmQnGmavV> + (Cm2 Gm Vg Cg2 Gg2kl2-2Cm Gm Vg2 Cg2 Gg2klavVv+2 Vm Cm Gm VgCg GgklXX k3 -2VmCmGm2VgCgGgklcvVv+av2 V?VgCgGg-2^avV*VgCgGgCmGmX\k3+2Vmav2 V? VgCgGgCmGm

//(2ИяОи<Змї%<і<%),

йу ft Kg CgGg,

? 4 Vm Cm Qrri Vg Cg Ggav ft Ш)

JM 4

Ge

HDaGfoKgCgGgU-flvftKgCgGg-ftiOKGA^

-2 0nG^Kg2Cg2Gg2jtIflvft + 2ftiG42G^3rgCgGg^XlW-2№j0ji2 Gm2 VgCgGgklavft + av2 K>2Vg2 Cg2 Gg2 -2 ^flv ft Kg CgGg Cm Gm2\ik3+2l>hQv2 ft2 VgCgGg Оті Gm + Vm2 Cm2 Gm4X\2k32+2Vm2 On2 Gm3Uk3avK> iYl

.2.

KCmGmVgCgGgkl

1/(2 Cm Gm Vg CgGg Vm),

+ GmVm C4e

+ fti2 On Gm2 a2 W2 - 4 Vm Cm Gm2 Vg Cg Gg av ft X k3) + av ft VgCgGg + Vm Cm Ст>1кЗ + ШОпОтач]Ь + (Ст2Ст Vg Cg Gg kl2-2CmGmVg Cg GgklavVv + 2^0?]2(friVgCgGgmtJtf-2fti0fl2VgCgGgCmGm2X[k3 +2ttnav2Vi>2VgCgGgOnGm + Vm2 Cm2 GmAX\2 k32 + 2Vm2 Cm2 GmX\k3 flvft + fti2 Cm2 Gm2 a2 ft2 !/(2VmCmGmVgCgGgl

-CIVgGg)

f(VgGg)

-4 Vm Cm Gm VgCgGgavVvXk3) )