THEORETICAL PHYSICS
AULA A2
MONDAY
THURSDAY
:
:
9:30
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AULA
BELTRAMI
Marco
-
gherardi
umpv.d@unimi.it
@
SYLLABVS
DI ME tuttora L
1.
SCALING Argument ,
)
Dynamics Systems ( CHAI
2.
3
ANALYSIS
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4.
VARIATIONAl PRINCIPLES
THERMO
DYNAMICS
( OPTIMIZATION )
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vedi video YT
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also the book
LA GRANGIA
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Classi col Mechanics
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HAMILTON IAN MEUHPNKS
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https://ocw.mit.edu/courses/
8-333-statistical-mechanics-istatistical-mechanics-ofparticles-fall-2013/pages/
lecture-notes/
ÌIRST
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05/12/2022
ti
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l
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why ieri ?
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diff
.
with
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themis
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i. reo
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lle
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il
→
.
il
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o
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e
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=
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In eden to
fixed and
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o
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e
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pere
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function
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,
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hey
→
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function
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integrate
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15/12/2022
Let' s
(
L
È)
"
92
.
.
.
.
9
.
.
n
9,
,
9
i
.
,
.
.
.
.
Attese
of
COORDINATE S
PREUVES
THE
GENERALI
D:
TED
Veloures
and
they
,
Why owly
e.
5
L
•
with
(q
L
=
,
is
which
×
I
.
free particle
a
.
.
.
.
.
9¢
.
.
.
.
,
the
generali zed
L
not
is
9in
A : It' s just
like this
like
,
lagrangiani Mechanics
e
Convention
for
.
.
1-2
=
,
mi
to
Charity
the
%
( mt )
0
,
p
=
'
2
u n>
in
the
on
o
/
.
p
=
net defend
has
d. o
≥
.
.
.
:
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o
Particle 's position
particle 's
Velocity
In )
.
.
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in
ID
example
write the E
p constant
In
✗
f
.
,
.
L
.
we
i
on
eq
nn>
can see
.
,
for
that
but not
on
this L
X
.
( Shipping
serve
per ) :
.
does not dependent
if the lagrangiani
momentum di L=p ) Constant
so
,
is
L da "
on
-
,
free particle
'
by hyp
È
,
,
=
,
-
concept let's
general
ID
final lagrangiani dcpeuds
our
mi
in
coord
dependent
g.
(
0 F
2M D.
are
I
this
(
.
.
System
e.
? Not
system
our
Then
.
can
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Basic coordinate
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Chomet
coords and velocità
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consimili
irnptnnnt
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also and etc ?
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la )
.
.
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|
coord
are
ASSOCIATED VELOUTIES
GENERALI 2- ED
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freedom
degree s of
the
✓
✓
muhomics
?
of FREEDOM
'
91
lagrangiani
about
things
DEGREEs
ARE THE
WHAT
•
just tuo
sey
.
fact
we
know that momentum p is
quanti ty far fneemotion-co.se
.
a
.
conslmed
,
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for
Generalizia
l
Pa
Let'
1
( 91
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Pk
In )
L
)
=
q
is
a
coNSERvEDavaNTHY_
,
generali zed momentum
:
do
s
.
.
general
the
EE
come
:
.
Gct
eq
Motion
of
.
of
mass
a
¥
spring
a
on
.
✗
2
=
0
.
"
ATWOOD
MACHINE
s
motion
Gct Eq of
.
untny down
E. L
.
cq
&
.
•
,
what
are
the coordinate share
Llx
( il
metter
L (t
Iii )
×
.
.
.
i. ii. )
.
of Writing
.
he
il try
,
l
E. L
.
eq
.
fa
and
fa
V
Mi
/
ma
by dchetùy
la write it
using
write the
?
the relation atween
for this lagrangiani
i
✗ a. ✗
M
.
.
i
Ma
.
Solutions
1
(
.
=
K U
lagrangiani
-
K { mi
'
=
U
=
{
te
(
2
✗
=
↓
un
i
'
.
{
k
2
✗
I
not K but
Classic Constant
,
{
>
a
il
i
=
mi
E. i.
=
-
kx
eq
→
.
I J; l
=
alt
the Solutions
ore
oscillato ry solutions
.
(
sin
and
→
mi
=
-
kx
equation
on
✗
note :
J✗ L
cos
.
.
.
)
of
motion
of
harmonic oscillatori
2
note
.
L
K
=
K
U
-
U
t.lk il ¢+4)
+
Total Kinetic energy
system 's
Total
-
her
-
system's
-
=
:
.
k
!
=
M
Ì?
,
to
U
✓
m
-
=
li K
L ↓
:
l
=
✗
×
g
,
{
.
+ ✗
i.
ma
+
2)
+
✗
→
a
+
a
a
glm
+
×
I
{
{(
=
di
L
m
×
,
_
"
=
(mi
)
è
me
+
+
mi
g(
m
m
t.us Kino
rbitmly
of
{ i.
Let's discuss
,
b-
=
=
✗
=
,
g(
m
hind
mossa
to
this
what
is
-
ne
e. i.
:
mah )
)
>
=
Q
:
A
:
Hon
In
✗
muy
µ
L
cani
Mnemba that
muy
.
u
→
(m
+
,
this
,
con
me
ohmgs
strani ts
com
we
'
"
mi
degree of freedom
conrtreùt
Amy
"
do
ii.
I
=
gfm
-
,
me
?
have
of
of
d
'
just
the
=
number
d.
{
)
-
do such valutativi
kill
have
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)
◦
.
f.
the end
.
.
0
( note
,
and we have to
F;
.
:
L
(×
]
,
ti )
]
masses on
'
.
.
:
rape
'
to discuss a oonsrtraint
b
a
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meus
iii-gIEI-fd-ay-J.it
non
do
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ore
the
mi
-
,
°
the
←t%
f- In tua
a
i.
-
the
.
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%
quel
we can
put
choose Whore to
↓
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+ ma
,
.
→
X
.
problems
.
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ma ✗
b
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:
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+
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circhi
mai :)
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,
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s
ve
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NE-EEEEE.li
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K and V.
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12
/ 2023
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Recall
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fine
v
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this kinder concepts
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Universalis
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macroscopici cynotwns
cane
insensibile to the microscopio
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