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成大機械系 高等動力學 專題討論
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OMG!
(ex.)
(ex.)
A:
B: Lagrange()
C:
Python
DEMO
nutationprecession
1. xyzbodyspace?xyzbodyBody:bodyxyz?
?
=
+
L
L=I
?non-inertialb (body)inertials (space)spacessspacebody??
sspace framexyzbodysspace?
body framebody?()?
(strap-down angular rate sensor)? body frame???! ???
bodyspace?
b?
b???
bs?
?
- ?
=
A Rodrigues rotation formulaCayley-Klein parameters
body framespace framesbody framespace frame
sdt=dsspacebody
sb frames frame
sdt=dssb
s
body xyzLIdiagonals frame b frameti -> ti+1
ti
ti+1
tibzSzti+1bz
Body xyz=
=
+
ti
ti+1
sb frameti+1 , ti+2s frame
b(t0)xyz(t0)
(1)=CK(b(t0)dt) (0)
ti+1
ti+2
ti+1
ti+2
lab frame
sspaces frameti!!bt+dtst
Sz (t1)b(t1)
ii+1
lab frame
(direction cosine matrix)
(ps. )
Lagrange
? pythonLagrange!
B Lagrange Equation
A Recursive Newton-Euler Equation
C
Python3D
B method
LagraneEuler Anglesreduce
Demo Lagranges method
BProf. HasbunClassical Mechanics with Matlab Applications matlab code.
Show top.py file.
!! 0!!!
Matlab
ODE solver
Demo Lagranges method
Run file Gyroscope-TeachDemo-1.py
xyzomegaL
ARecursive NE equation
ARecursive NE equation
EulerDCMiter()
ODE
Lagrange
ARecursive NE equation
Demo ring motion (5,8,0)wave motion (5,0,-4)
Demo space cone body cone, file Gyro_spaceBodyCone.py
body coneconezwwL
Demo file Gyroscope-TeachDemo-2-circular.py
ADEMO-1
A?
(!)
090sin cos!!!!!
?
AB
ABNEvs Lagrange
Run file Gyroscope-TeachDemo-3.pyDrawOption?
580,50-4,400
numerical drift
bodylab
A
BLagrange(t)(t)(t)
Bb(t)cBc
B
EulerW2bodyW()
B
A? C!!
directDCMiter()
? AC-AC
DEMO-3
BCLagrangevs
Run file Gyroscope-TeachDemo-4.py
A
PCICgyro sensorPortable device
C
Lagrange
GPSfusion
(Kalman filter)
?
IncludeNoiseInOmega(1)
Show and run Gyroscope-TeachDemo-5.py
1 ~ -1 rad/sec 1 rad/sec = 57 deg / sec
2000Hz-> (~MHz)
J-cycle
2014/1 6/MPU6050
0.01
:
http://blog.sina.com.cn/zhaowenwin
bodybody
(tsb frame)body
=
body xyzbody xyz
NE
2
gyro sensor
http://whymranderson.blogspot.tw/2014/03/4th-runge-kutta.html
!
?