Question

In: Physics

In simple terms (so a non-physicist with an upper division math background can understand), what is...

In simple terms (so a non-physicist with an upper division math background can understand), what is a Lagrangian and what is it used for?

Solutions

Expert Solution

Lagrangian function, also called Lagrangian, quantity that characterizes the state of a physical system. In mechanics, the Lagrangian function is just the kinetic energy (energy of motion) minus the potential energy (energy of position).

One may think of a physical system, changing as time goes on from one state or configuration to another, as progressing along a particular evolutionary path, and ask, from this point of view, why it selects that particular path out of all the paths imaginable. The answer is that the physical system sums the values of its Lagrangian function for all the points along each imaginable path and then selects that path with the smallest result. This answer suggests that the Lagrangian function measures something analogous to increments of distance, in which case one may say, in an abstract way, that physical systems always take the shortest paths.

In the special case of a ray of light, the path of system configurations is just the ordinary path of the light through space, and the Lagrangian function reduces simply to a measure of the passage of time. The particular curved path that a light ray takes through a refracting lens is therefore just the one that takes the least time.

The principle is, however, much more general than that, and it is a remarkable discovery that it seems to describe all phenomena equally well, including, for example, the travel of a rocket to the moon, and the likelihood that colliding subatomic particles will scatter each other in selected directions.

I hope it was helpful.. please rate me positive..


Related Solutions

Please use simple terms so I can understand better. thanks! Why do cells need to multiply?...
Please use simple terms so I can understand better. thanks! Why do cells need to multiply? Discuss a few reasons. Try to do this without using the word “reproduction” or “reproduce”. Define homologous chromosomes Discuss the chromosomal number of cells before mitosis and after mitosis Is mitosis involved in asexual reproduction? What are telomeres and why are they important? How does cytokinesis (cytoplasmic division) differ in animal cells vs plant cells? Define oncogene, proto-oncogene, neoplasm, tumor, and metastasis
Value of a Statistical Life (VSL). (a) Describe VSL in terms that a non-economist can understand....
Value of a Statistical Life (VSL). (a) Describe VSL in terms that a non-economist can understand. (b) Lavetti (2017) studies the wage-risk tradeoff for one of the riskiest professions in the United States, crab fishing in Alaska. The riskiness of crab fishing is driven mainly by the season and weather conditions. Lavetti collects data on the weather conditions of specific fishing trips, and the wages paid to the crew. He then runs a regression of the wage on the expected...
proximal upper extremities what are they? how would you define them in non medical terms?
proximal upper extremities what are they? how would you define them in non medical terms?
in JAVA: implement a class called tree (from scratch) please be simple so i can understand...
in JAVA: implement a class called tree (from scratch) please be simple so i can understand thanks! tree(root) node(value, leftchild,rightchild) method: insert(value)
Explain is a super simple way--so a 6th grader would understand: What is primary data? How...
Explain is a super simple way--so a 6th grader would understand: What is primary data? How is that different from secondary data? Would you use primary data or secondary data (or both) to gather information about your target population for your own program? (Remember to include a "for real" example)
Can you please write this in python and comment as well so I can understand what...
Can you please write this in python and comment as well so I can understand what yo are doing. Thank you. 1)Loop through list A, at each iteration, show the square root result of that element. Add proper text to your print function. A = [-4, 1, -16, 36, -49, 64, -128] 2)Create a counter variable, name it i and initialize it to 0. Using a for loop, count how many numbers are divisible by 3 in range of 1...
In what ways can non-current assets be disposed? What do you understand by the trade in...
In what ways can non-current assets be disposed? What do you understand by the trade in disposal? Trust in him Enterprise has the following tasks at 1st April, 2017. NO. TRUCK NUMBER DATE ACQUIRED COST OF VEHICLE GHȻ ESTIMATE RESIDUAL VALUE GHȻ ESTIMATED USEFUL LIFE 1 GT 124516 1st October, 2016 42,500.00 12,500.00 Five (5) years NO. TRUCK NUMBER DATE ACQUIRED COST OF VEHICLE GHȻ ESTIMATE RESIDUAL VALUE GHȻ ESTIMATED USEFUL LIFE 2. GT 346717 1st April, 2017 60,000.00 10,000.00...
Background on cell division in plants: Why is cell division a regulated process? What is known...
Background on cell division in plants: Why is cell division a regulated process? What is known about division plane orientation in plants? Please explain in detail! I'll upvote
Background on cell division in plants: Why is cell division a regulated process? What is known...
Background on cell division in plants: Why is cell division a regulated process? What is known about division plane orientation in plants? Please explain in detail not wikipedia! I'll upvote
Discuss/explain in simple to understand terms what does the p-value represent for any hypothesis test procedure...
Discuss/explain in simple to understand terms what does the p-value represent for any hypothesis test procedure and why is it important to report the p-value when presenting the findings of a test/research. Include in your discussion a specific example you find online for context. (Do not just repeat one similar to another student's example).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT