magnus force in ressistance enviroment
TRANSCRIPT
1
Dynamics and resistance of enviorment
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1(
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1(
2
22
22
2
22
2
2
2
2
2
22
22
2
22
2
2
2
2
2
2
2
22
2
22
2
2
2
2
tCostCosr
tSinhrdt
dx
dt
dh
dt
dy
dt
dh
dt
dz
dt
zd
dt
yd
dt
xd
dt
zdm
directionz
tCostSinr
tCoshrdt
dz
dt
dr
dt
dx
dt
dh
dt
dy
dt
zd
dt
yd
dt
xd
dt
ydm
directiony
tCostSinr
tCoshrdt
dy
dt
dr
dt
dz
dt
dh
dt
dx
dt
zd
dt
yd
dt
xd
dt
xdm
directionx
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(
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(
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2
22
2
2
22
2
2
22
2
txtCostSinrtCoshrdt
dz
dt
dr
dt
dx
dt
dh
tytCostSinrtCoshrdt
dy
dt
dr
dt
dz
dt
dh
dt
d
dt
dJJ
dt
dJ
tztCostSinrtCoshrdt
dy
dt
dh
dt
dz
dt
dh
txtCostCosrtSinhrdt
dx
dt
dh
dt
dy
dt
dh
dt
d
dt
dJJ
dt
dJ
tytCostCosrthSinrdt
dx
dt
dh
dt
dy
dt
dh
tztCostSinrtCoshrdt
dz
dt
dh
dt
dx
dt
dr
dt
d
dt
dJJ
dt
dJ
yxz
xzy
zyx
2
Magnus forces
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1tAtxtvF iii
Scalar projected;
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1 222
22
2
22
2
2
tCostSinrthCosrdt
dx
dt
zd
dt
yd
dt
xd
]][[]])[[]][[2)()()()(2
1 222
22
2
22
2
2
tCostSinrthCosrdt
dy
dt
zd
dt
yd
dt
xdFy
]][[]])[[]][[2)()()()(2
1 222
22
2
22
2
2
tCostCosrthSinrdt
dz
dt
zd
dt
yd
dt
xdFz
3,1]],[][][[)]([ ittrtvSinrtvmF iiiiiii ;
3
kdt
dx
dt
dh
dt
dy
dt
dhj
dt
dz
dt
dr
dt
dx
dt
dhi
dt
dy
dt
dr
dt
dz
dt
dhmAF ii )
22()
2()
2(
;
Crossections of resistance
]][[]])[[]][[2(
]][[])[]][[2(
][[]])[[]][[2(
2
2
2
tCostCosrtSinhr
tCosSinrtCoshr
tCostSinrtCoshr
Ai
’
Force-(Magnus)
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]][[])[][2(
]][[])[][2(
2/12
2
2
tCosCosrhSinr
tCosSinrhCosr
tCosSinrhCosr
Fi
Det
dt
dh
dt
dr
dt
dr
dt
dz
dt
dy
dt
dxkji
2
Scalar projected Magnus momentus
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(
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(
]];[[]])[[]][[2)(2
(
2
2
2
tCosCosrtSinhrdt
dx
dt
dh
dt
dy
dt
dhmF
tCosSinrtCoshrdt
dz
dt
dr
dt
dx
dt
dhmF
tCostSinrtCoshrdt
dy
dt
dr
dt
dz
dt
dhmF
Mz
My
Mx
Momentum and Oiler equation as function of time
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2
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12
3
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][][3][][
12
3
222
2222
2222
tytxmCosCos
rmJ
tztxmCosCos
hrmJ
tztymCosCos
hrmJ
z
y
x
Final form of equations, projected in 6 directions.
k
dt
dx dt
dy dt
dz
dt
dr
dt
dr
dt
dh 2
ij
4
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2
2
2
22
2
22
2
2
2
2
2
2
2
22
2
22
2
2
2
2
txtCostSinrthCosrdt
tdz
dt
tdr
dt
tdx
dt
tdh
tytCostSinrthCosrdt
dy
dt
dr
dt
dz
dt
dhdt
td
dt
tdtztxmCosCos
hrm
tztymCosCos
hrm
dt
dtytxmCosCos
rm
tztCostSinrthCosrdt
tdy
dt
tdh
dt
tdz
dt
tdh
txtCostCosrthSinrdt
tdx
dt
tdh
dt
tdy
dt
tdhdt
td
dt
tdtztymtCostCos
hrm
tytxmCosCos
rm
dt
tdtztxmCosCos
hrm
tytCostCosrthSinrdt
tdx
dt
tdh
dt
tdy
dt
tdh
tztCostSinrthCosrdt
tdz
dt
tdh
dt
tdx
dt
tdr
dt
td
dt
tdtytxmCosCos
rm
tztxmCosCos
hrm
dt
dtztymCosCos
hrm
tCostCosrthSinr
dt
tdx
dt
tdh
dt
tdy
dt
tdh
dt
dz
dt
tzd
dt
tyd
dt
txd
dt
tzdm
tCostSinrthCosr
dt
tdz
dt
tdr
dt
tdx
dt
tdh
dt
tdy
dt
tzd
dt
tyd
dt
txd
dt
tydm
tCostSinrthCosr
dt
tdy
dt
tdr
dt
tdz
dt
tdh
dt
tdx
dt
tzd
dt
tyd
dt
txd
dt
txdm
osezMoment
oseyMoment
osexMoment
directionz
pravacy
directionx