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00:00:02
question which talks about the multipliers
00:00:05
on the left so it is the
00:00:08
most interesting question of this exercise
00:00:11
so 5 you should know that in this
00:00:18
exercise
00:00:19
we are going to see the technique so the
00:00:22
technique of calculation
00:00:23
ok but it you should know that this concept of
00:00:27
multiplier on the left is a
00:00:28
mathematical concept and in mechanics
00:00:32
for example we can use the
00:00:35
multipliers of the barn to give
00:00:37
for example the expression of the
00:00:41
generalized forces that we therefore have in order to grasp
00:00:47
a small little it is
00:00:50
language multiplier we are going to make a comparison
00:00:52
between the ordinary method and this
00:00:57
method of multipliers of the
00:01:01
branch so first for the
00:01:03
ordinary method roughly for the
00:01:07
ordinary method we are going to consider that the
00:01:10
connections that we have as being
00:01:13
main reasons and we take the number of
00:01:18
degrees of freedom
00:01:21
if we consider our constraints as
00:01:23
being main to obtain the number
00:01:27
of degrees of freedom made the number
00:01:29
of configuration parameters - the
00:01:33
number of constraints and the number of
00:01:37
degrees of freedom equal exactly in
00:01:40
number of the equations on the left that we
00:01:41
have so if we take into consideration if
00:01:46
we consider that the constraints its
00:01:48
main the equations of the barn
00:01:51
will be reduced automatically
00:01:53
so you will understand what I am
00:01:56
saying therefore for the method originating so
00:02:01
for example in this exercise
00:02:03
so in art we consider the
00:02:11
kona connections so we have here connections which are x
00:02:15
to - r of state - xb equal to zero so that
00:02:22
so we have this season we also have xb
00:02:25
plus hervy equal to zero so we will
00:02:29
consider that these connections are
00:02:31
mainly considered ten years
00:02:33
as main and we will take
00:02:46
and we will take two parameters which remain in
00:02:49
because before we had if we do
00:02:52
not consider these two connections main camp
00:02:57
we will work with four parameters
00:03:00
we go that including the case of the multipliers
00:03:03
on the left
00:03:04
my main and we take two
00:03:06
parameters
00:03:08
well these two parameters so for
00:03:11
example x a&t time and we have two
00:03:22
equations of the branch
00:03:30
which are your summer of dl / dx point
00:03:36
to - dl / dx to equal to zero and
00:03:43
summer sur of dl / of state point to heaps
00:03:48
point to details equal to zero but
00:03:54
here you have to know that we have two
00:03:56
equations with two unknowns so the
00:04:10
problem here is bookable these two
00:04:13
equations will give us your quite
00:04:15
simply therefore will give us
00:04:17
the expression of x at 2t and piles of tea
00:04:22
isn't it and if I want for example
00:04:27
the expression of xb of tea and girls of
00:04:30
tea well I just have to use these
00:04:33
two constraints that I have so this
00:04:36
constraint will imply
00:04:38
xb of tea equal to since I have already
00:04:42
found x to of t&t no doubt
00:04:44
using these two equations and this
00:04:47
expression will involve us daughter of
00:04:52
your with all simplicity in this case
00:04:55
you must know that in this case therefore
00:05:00
in this case there has consumed the
00:05:08
constraints
00:05:17
now that we are it of the method
00:05:20
of the multipliers of the left
00:05:22
I am going to call this equation 1 and
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this equation 2 therefore
00:05:43
branch multiplier method in the case of this
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method 1 and 2 are no longer considered
00:05:51
as main but are considered
00:05:54
as supplementary are considered
00:06:00
as supplementary in other words we
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will go and add therefore not four
00:06:09
equations which we will see as
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additional and we therefore take since
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we consider them as additional time
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we do not consume them well we will
00:06:26
simply work with the four
00:06:27
configuration parameters gones and
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take four parameters which are quite
00:06:37
simply icsa of state xb and daughter I'm going to take
00:06:45
this constraint and I'm going to call it
00:06:50
so let f1 equal to x at - r state - xv
00:06:59
and and f2 equal to xb plus and revit it's
00:07:06
very simple now we're going to give the
00:07:10
equations that we have the method of the
00:07:14
multipliers on the left in this case
00:07:17
we will have four
00:07:21
parameters here so what we will have given up
00:07:24
on was from dl / dx point to - dl / des
00:07:31
icsa but be careful here what we fact
00:07:35
it is a certain sum therefore equal here
00:07:40
in to two constraints since we have
00:07:45
constraints then we will have two
00:07:48
multiplier of the canche
00:07:50
the first so here we derive with
00:07:51
respect to x a therefore we have x a therefore in to
00:07:54
lambda a and we derive
00:07:56
the first constraint with respect to
00:08:24
up to 2 since
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we have here two constraints and if of course so rotten
00:08:33
it plays between 1 and 4 so
00:08:37
here we have four parameters
00:08:41
so we will see here on dttl on
00:08:48
point heads so you have
00:08:51
understood everything of course on debt is equal
00:08:54
so here we will see lambda 2 tf1 rather
00:08:59
slow blank of f1 on states plus
00:09:03
lambda of tf2 on times so I will
00:09:12
continue I will give the other
00:09:16
equations
00:09:40
so here these are the equations that we have
00:09:44
but there are one thing which is very
00:09:46
important for what concerns these
00:09:48
equations knows so here you have to
00:09:50
know that we have for the moment 4 so you
00:09:59
have to be careful
00:10:00
so here we have four equations with six
00:10:05
unknowns since here we have four
00:10:12
equations with six unknowns
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the number of equations is less than the
00:10:16
number of unknowns so for the moment
00:10:19
the problem is not resolvable, it is
00:10:28
for this reason that we must
00:10:30
also add these two constraints as to the
00:10:33
cde constrains these two constraints which
00:10:36
are considered as additional
00:10:38
here we have not consumed our accounts its
00:10:40
constraints but as soon as we consume these
00:10:42
constraints
00:10:44
we come across these two equations so
00:10:49
hence the interest we must add in addition to
00:10:52
these equations we must add these
00:10:58
two additional constraints
00:11:06
it is x b + hervy equal to zero and there we
00:11:12
come across six equations with six unknowns
00:11:20
so since we have that then the problem is
00:11:29
what and reasonable so it is without the
00:11:39
barn multiplier method
00:11:46
well I add a remark you should know
00:11:48
that without it's the generalized force
00:11:53
associated with
00:12:16
technique to give
00:12:19
equation of gombe using
00:12:22
language multipliers
00:12:23
so please just
00:12:26
do the calculations now so you
00:12:28
have to give me lambda one equal and lambda
00:12:32
2 equal

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l'énoncé de l'exercice https://www.facebook.com/unsupportedbrowser?_rdc=1&_rdr

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