Symmetries of Space andtime induce Jawad Cheayto
corresponding symmetries in
the Lagrangian
of a conservative holonomic system
These symmetries in turn allow us
to obtain conservation laws
forsome
physical quantities suchas energy and
momentum
Audio I
Space is homogeneous
Space is isotropic No possibility tosingleout a proffered direction
Time is homogeneous
System is isolated
conservativetholononic
2 0 East
System is isolated
81 0 underarbitrary
virtualspace translation
Audio3
Conservation
ofEnergy
Let E be a conservative holonomic system composed of N particles
We assumefurthermorethat the constraints Kconstraints holonomictime
independent
aretimeindependent x in initn so
ysits Xa gaita
Lf
f X
lyzits X2 gaita XnYn itn so
,Fkn yl Audio 4
It
In fact K U
E aapal9ir
xjiIjiYa
i.I7d
Zil9si
Zi
i9s
U Ul9u9a
I
Ms where a O
Y f Y 0 0 0
Audios
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ade's
adf.EE
da Esa 3 4 0
So Iggy L est
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Eda
f Eoin Ig
we have 0 since U UH as
Yg
so 9
YEE's Iq
We will admitfor the moment that
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Soas Iggy Iggy L est
then 2h1 Last
2h1 th U est
2h1 Kt Vest
hitUs est East
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corresponding symmetries in
the Lagrangian
of a conservative holonomic system
These symmetries in turn allow us
to obtain conservation laws
forsome
physical quantities suchas energy and
momentum
Audio I
Space is homogeneous
Space is isotropic No possibility tosingleout a proffered direction
Time is homogeneous
System is isolated
conservativetholononic
2 0 East
System is isolated
81 0 underarbitrary
virtualspace translation
Audio3
Conservation
ofEnergy
Let E be a conservative holonomic system composed of N particles
We assumefurthermorethat the constraints Kconstraints holonomictime
independent
aretimeindependent x in initn so
ysits Xa gaita
Lf
f X
lyzits X2 gaita XnYn itn so
,Fkn yl Audio 4
It
In fact K U
E aapal9ir
xjiIjiYa
i.I7d
Zil9si
Zi
i9s
U Ul9u9a
I
Ms where a O
Y f Y 0 0 0
Audios
dtdl4 df.lk ddcy
Asda 13kt gifts L
Efik dainty ii III living I'd
Ii CIg.oid ddf.Ei9aYg
, Audio6
ade's
adf.EE
da Esa 3 4 0
So Iggy L est
2L NH ul
Iga Join Eda 292
Eda
f Eoin Ig
we have 0 since U UH as
Yg
so 9
YEE's Iq
We will admitfor the moment that
gaia Jtg 2K
Soas Iggy Iggy L est
then 2h1 Last
2h1 th U est
2h1 Kt Vest
hitUs est East
, Goin h 2K Audio7 8
g
Recallthat the paapl9lgj9p
th 12 pa4Bl9l9I9p 8th2.3 s
Igg
joy
fgaaa.BY 9I9ptaaplalfg2g949pta4Bca19afg9jB
p
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p
L Epfaapcallsasciptoiasps Sastffitopf
t.EE a4plaKSx89pt9a8p8
aaspl919pt 19,8419ps
Ay as Ad8
12 SEEasa4i9at 49,84192 adpik9p ap.aoipd
layptap419
aa.sc Ga l
a'xp Aba Lg Agptapsd
