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gracie
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Please help, I've put this is true on my personal statement, but I'm now fairly sure that it is not, but a more expert opinion would be extremely helpful.
You are absolutely right, and it is embarrassing to know that I forgot to add the dots! As I punishment, I've written out the full procedures for Gracie.nasu said:The first term in that Lagrangian should have the derivatives of x and y in respect to time.
What about the opportunity for gacie to discover this for herself ? "Give it a try and PF will help you further..." Then it woudn't have been a waste either !Rescy said:Of course! Lagrangian is equivalent to Newton's second law of motion in Cartesian coordinates.
$$L= {1\over 2}m(x^2+y^2)-mgy$$ apply Euler-Lagrange equation for x and y and you derive a differential equation whose solutions are SUVAT.
It is a waste for Lagrangian Mechanics to be applied on SUVAT!
May I ask if you are applying to UK or US?gracie said:Thank you so much everybody, I thought I knew the answer but wanted proof from experts, I really appreciate it :)
BvU said:Hello Gracie, welcome to PF !
Impressed you should be concerned with Lagrangians at 17 !
But, to answer your question: yes you can. Simply write down the Lagrangian and then the Lagrange equations of motion follow.
Give it a try and PF will help you further...
Rescy said:May I ask if you are applying to UK or US?
BvU said:Hello Gracie, welcome to PF !
Impressed you should be concerned with Lagrangians at 17 !
But, to answer your question: yes you can. Simply write down the Lagrangian and then the Lagrange equations of motion follow.
Give it a try and PF will help you further...
And how can one derive distance, initial velocity and time, knowing only the lagrangian?BvU said:Google to the rescue:
s = distance (metres, m)
u = initial velocity (metres per second, ms^-1)
v = final velocity (metres per second, ms^-1)
a = acceleration (metres per second squared, ms^-2)
t = time (seconds, s)
A Langrangian is a mathematical function that describes the dynamics of a system in classical mechanics. It is used to derive the equations of motion for a system, such as the SUVAT equations.
The SUVAT equations can be derived using the Euler-Lagrange equations, which are a set of equations that relate the Lagrangian of a system to its equations of motion. By setting up the Lagrangian for a system and applying the Euler-Lagrange equations, the SUVAT equations can be obtained.
Using a Langrangian to derive the SUVAT equations allows for a more systematic and elegant approach compared to using traditional methods, such as Newton's laws. It also allows for the inclusion of constraints and more complex systems.
No, the SUVAT equations are just one example of equations that can be derived using a Langrangian. The Langrangian method can be applied to a wide range of physical systems, including those with multiple particles and forces.
No, the SUVAT equations can also be derived using other methods, such as using Newton's laws or conservation of energy. However, using a Langrangian can provide a more elegant and comprehensive understanding of the underlying principles behind the equations.