周期関数時間e

rac2φc'
Sac=(1/2)rac2φc'
dSac/dt={(1/2)rac2φc'}'=racrac'φc'+(1/2)rac2φc''
rac'φc'+(1/2)racφc''=0

B
Xb
A
Vxba
αxba
Yb
A
Vyba
αyba
Xb
C
Vxbc
αxbc
Yb
C
Vybc
αybc
A
(xba,yba)=(rbacosφa,rbasinφba)
C
(xbc,ybc)=(rbccosφc,rbcsinφbc)

ma*dVxa/dt=fxa=f(ra)cosφa
ma*dVya/dt=fya=f(ra)sinφa

Vxa=dxa/dt=ra'cosφa–raφa'sinφa
Vya=dya/dt=ra'sinφa+raφa'cosφa

αxa
αxa=dVxa/dt
αxa=ra''cosφa–ra'φa'sinφa–ra'(φa'sinφa)–ra(φa'sinφa)'
αxa=racosφa–ra'φa'sinφa–ra'(φa'sinφa)–ra(φasinφa+(φa')2cosφa)
αxa=ra''cosφa–ra'φa'sinφa–ra'φa'sinφa–ra'φa'sinφa–ra(φa')2cosφa
αxa=r'a'cosφa-2ra'φa'sinφa–ra'φa'sinφa–ra(φa')2cosφa

αya
αya=dVya/dt
αya=ra''sinφa+ra'φa'cosφa+ra'(φa'cosφa)+ra(φa'cosφa)'
αya=rasinφa+ra'φa'cosφa+ra'φa'cosφa+ra(φacosφa-(φa')2sinφa)
αya=ra''sinφa+ra'φa'cosφa+ra'φa'cosφa+ra'φa'cosφa–ra(φa')2sinφa
αya=ra''sinφa+2ra'φa'cosφa+ra'φa'cosφa–ra(φa')2sinφa

cosφa+sinφa=ma(cosφa*dVxa/dt+sinφa*dVya/dt)=(sin2φa+cos2φa)f(ra)=f(ra)
cosφa*dVxa/dt+sinφa*dVya/dt=f(ra)/ma
sinφa–cosφa=ma(sinφa*dVxa/dt+cosφa*dVya/dt)=cosφasinφaf(ra)-sinφacosφaf(ra)=0

dVxa/dt
dVya/dt
cosφa{ra''cosφa–2ra'φa'sinφa–ra'φa'sinφa-ra(φa')2cosφa}+
sinφa{rasinφa+2ra'φa'cosφa+ra'φa'cosφa–ra(φa')2sinφa}=ra–ra(φa')2=f(ra)/m
ma{ra''–ra(φa')2}=f(ra)

sinφa{ra''cosφa-2ra'φa'sinφa–ra'φa'sinφa–ra(φa')2cosφa}-
cosφa{rasinφa+2ra'φa'cosφa+ra'φa'cosφa–ra(φa')2sinφa}=2ra'φa'+raφa=0
ma(2ra'φa'+raφa'')=0

ma{ra''–ra(φa')2}=f(ra)
ma(2ra'φa'+raφa'')=0

ra2φa'

B
A
Sba=(1/2)rba2φba'
dSba/dt={(1/2)rba2φba'}'=rba rba'φba'+(1/2)rba2φba''　
rba'φba'+(1/2)rbaφba''=0

B
C
Sbc=(1/2)rbc2φc'
dSbc/dt={(1/2)rbc2φbc'}'=rbcrbc'φbc'+(1/2)rbc2φbc''　
rbc'φbc'+(1/2)rbcφbc''=0

f(ra)
f(rb)
f(rc)
dφ/dt=hu^2

1/ra
1/rb
1/rc

ua
ub
uc

{(d^2u)/(dφ^2)}=f(1/u)/(h^2u^2)

Δφa/Δt=haua^2
Δφb/Δt=hbub^2
Δφc/Δt=hcuc^2

1/ra
1/rb
1/rc

ua
ub
uc

f(ra)
f(rb)
f(rc)

{(ΔΔua)/(Δφa^2)}=f(1/ua)/(ha^2ua^2)
{(ΔΔub)/(Δφb^2)}=f(1/ub)/(hb^2ub^2)
{(ΔΔuc)/(Δφc^2)}=f(1/uc)/(hc^2uc^2)

ra=1/ua=La/{1+eacos(φa-φa)}
rb=1/ub=Lb/{1+ebcos(φb-φb)}
rc=1/uc=Lc/{1+eccos(φc-φc)}

φ
e
φa
φb
φc

最終更新:2018-08-25 20:10:38
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