General Jawad Cheayto
Coordinates
Holonomic
Constraints
Non Holonomic
System of N particles
p
fu Xsly its Xnyn tn t O
3N Cartesian coordinates
h constraints 3N has
X2 Zz Xn
YnZn
e
Y
si numbers ofdegrees
So we need s generalized offreedom
the
of
system
coordinates
to describethe
the
configuration
of system
at anygivenmoment
of time
, Lagrangian Audio 2
Mechanics
Let E be a mechanical
system composed of Nparticles
subject toKeholononicconstraints
All constraints are holonomic
All applied forces actingon
the system are assumed
1 Subdivision
conservative of forces into
Constraintforces and appliedforces
Constraintforce Due to the presence
a constraints Constraintforces theirexistence depends
of
on otherforces
Appliedforce forces notdue to gfonstraint
a constraints
it canchangethe rt
the
by charge of
massorte length the
Generalized coordinates spring
of veg
applied
911 gs where s 3N force
xi filgu.o.o.gs't T
gs.tt gTEEIrI
yi.g.iq
rTu. Ziehi
9ne.ee 9s t 2 1 is
,Derivation
ofthe Audio3
Lagrangian equations
firstDerivation Variational
principle
Action
If E has s degrees
of
freedom it hasgeneralized
coordinates
q As
Assumethat E starts with a
configuration
qui ai at tests
and ends at a
configuration
gin qY at Tst
Audio y
q
9
qui fff
i r
Along
Definseq
p
path
aff
ca asia iasitHt
f
te ta along a certain
Path19
9s tt 4944 gg b
where dga
dt
, Liske Lagrangianof
the where H
system
z1y Miu
K U
kinetic potential i mass
my
energy energy
Let E'bete total applied
force acting on the particle i
ten No potential energyfor
E gTadiU constraint forces
Ei
iii YI't'S.IT Hi
Audios
rEIX.IIy.jo ziIig
positionvector
offeparticlei
1
Audio 7
Leastaction 2 s
Principle
choosingmakes
that
A system E evolves between two path
settled or minimal
lattimets and
configurations
S Edt is
extremal
HEYattimeta sothat theaction
Coordinates
Holonomic
Constraints
Non Holonomic
System of N particles
p
fu Xsly its Xnyn tn t O
3N Cartesian coordinates
h constraints 3N has
X2 Zz Xn
YnZn
e
Y
si numbers ofdegrees
So we need s generalized offreedom
the
of
system
coordinates
to describethe
the
configuration
of system
at anygivenmoment
of time
, Lagrangian Audio 2
Mechanics
Let E be a mechanical
system composed of Nparticles
subject toKeholononicconstraints
All constraints are holonomic
All applied forces actingon
the system are assumed
1 Subdivision
conservative of forces into
Constraintforces and appliedforces
Constraintforce Due to the presence
a constraints Constraintforces theirexistence depends
of
on otherforces
Appliedforce forces notdue to gfonstraint
a constraints
it canchangethe rt
the
by charge of
massorte length the
Generalized coordinates spring
of veg
applied
911 gs where s 3N force
xi filgu.o.o.gs't T
gs.tt gTEEIrI
yi.g.iq
rTu. Ziehi
9ne.ee 9s t 2 1 is
,Derivation
ofthe Audio3
Lagrangian equations
firstDerivation Variational
principle
Action
If E has s degrees
of
freedom it hasgeneralized
coordinates
q As
Assumethat E starts with a
configuration
qui ai at tests
and ends at a
configuration
gin qY at Tst
Audio y
q
9
qui fff
i r
Along
Definseq
p
path
aff
ca asia iasitHt
f
te ta along a certain
Path19
9s tt 4944 gg b
where dga
dt
, Liske Lagrangianof
the where H
system
z1y Miu
K U
kinetic potential i mass
my
energy energy
Let E'bete total applied
force acting on the particle i
ten No potential energyfor
E gTadiU constraint forces
Ei
iii YI't'S.IT Hi
Audios
rEIX.IIy.jo ziIig
positionvector
offeparticlei
1
Audio 7
Leastaction 2 s
Principle
choosingmakes
that
A system E evolves between two path
settled or minimal
lattimets and
configurations
S Edt is
extremal
HEYattimeta sothat theaction
