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[COURS] ENJOY THE NIGHT de Gwendoline HOPIN & Adela ROBAK, enseignée par Lilly WEST

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00:00:02

question which talks about the multipliers

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on the left so it is the

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most interesting question of this exercise

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so 5 you should know that in this

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exercise

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we are going to see the technique so the

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technique of calculation

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ok but it you should know that this concept of

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multiplier on the left is a

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mathematical concept and in mechanics

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for example we can use the

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multipliers of the barn to give

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for example the expression of the

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generalized forces that we therefore have in order to grasp

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a small little it is

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language multiplier we are going to make a comparison

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between the ordinary method and this

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method of multipliers of the

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branch so first for the

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ordinary method roughly for the

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ordinary method we are going to consider that the

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connections that we have as being

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main reasons and we take the number of

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degrees of freedom

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if we consider our constraints as

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being main to obtain the number

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of degrees of freedom made the number

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of configuration parameters - the

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number of constraints and the number of

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degrees of freedom equal exactly in

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number of the equations on the left that we

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have so if we take into consideration if

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we consider that the constraints its

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main the equations of the barn

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will be reduced automatically

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so you will understand what I am

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saying therefore for the method originating so

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for example in this exercise

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so in art we consider the

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kona connections so we have here connections which are x

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to - r of state - xb equal to zero so that

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so we have this season we also have xb

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plus hervy equal to zero so we will

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consider that these connections are

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mainly considered ten years

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as main and we will take

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and we will take two parameters which remain in

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because before we had if we do

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not consider these two connections main camp

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we will work with four parameters

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we go that including the case of the multipliers

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on the left

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my main and we take two

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parameters

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well these two parameters so for

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example x a&t time and we have two

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equations of the branch

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which are your summer of dl / dx point

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to - dl / dx to equal to zero and

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summer sur of dl / of state point to heaps

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point to details equal to zero but

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here you have to know that we have two

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equations with two unknowns so the

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problem here is bookable these two

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equations will give us your quite

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simply therefore will give us

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the expression of x at 2t and piles of tea

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isn't it and if I want for example

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the expression of xb of tea and girls of

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tea well I just have to use these

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two constraints that I have so this

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constraint will imply

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xb of tea equal to since I have already

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found x to of t&t no doubt

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using these two equations and this

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expression will involve us daughter of

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your with all simplicity in this case

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you must know that in this case therefore

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in this case there has consumed the

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constraints

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now that we are it of the method

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of the multipliers of the left

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I am going to call this equation 1 and

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this equation 2 therefore

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branch multiplier method in the case of this

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method 1 and 2 are no longer considered

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as main but are considered

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as supplementary are considered

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as supplementary in other words we

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will go and add therefore not four

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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

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simply work with the four

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configuration parameters gones and

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take four parameters which are quite

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simply icsa of state xb and daughter I'm going to take

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this constraint and I'm going to call it

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so let f1 equal to x at - r state - xv

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and and f2 equal to xb plus and revit it's

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very simple now we're going to give the

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equations that we have the method of the

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multipliers on the left in this case

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we will have four

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parameters here so what we will have given up

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on was from dl / dx point to - dl / des

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icsa but be careful here what we fact

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it is a certain sum therefore equal here

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in to two constraints since we have

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constraints then we will have two

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multiplier of the canche

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the first so here we derive with

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respect to x a therefore we have x a therefore in to

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lambda a and we derive

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the first constraint with respect to

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up to 2 since

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we have here two constraints and if of course so rotten

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it plays between 1 and 4 so

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here we have four parameters

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so we will see here on dttl on

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point heads so you have

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understood everything of course on debt is equal

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so here we will see lambda 2 tf1 rather

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slow blank of f1 on states plus

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lambda of tf2 on times so I will

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continue I will give the other

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equations

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so here these are the equations that we have

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but there are one thing which is very

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important for what concerns these

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equations knows so here you have to

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know that we have for the moment 4 so you

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have to be careful

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so here we have four equations with six

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unknowns since here we have four

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equations with six unknowns

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the number of equations is less than the

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number of unknowns so for the moment

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the problem is not resolvable, it is

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for this reason that we must

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also add these two constraints as to the

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cde constrains these two constraints which

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are considered as additional

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here we have not consumed our accounts its

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constraints but as soon as we consume these

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constraints

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we come across these two equations so

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hence the interest we must add in addition to

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these equations we must add these

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two additional constraints

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it is x b + hervy equal to zero and there we

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come across six equations with six unknowns

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so since we have that then the problem is

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what and reasonable so it is without the

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barn multiplier method

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well I add a remark you should know

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that without it's the generalized force

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associated with

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technique to give

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equation of gombe using

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language multipliers

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so please just

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do the calculations now so you

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have to give me lambda one equal and lambda

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2 equal

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