Function of Higher Order Derivative Type 2) Problem 1

TL;DR

This video discusses type 2 of calculus of variation, which involves problems with function of higher order derivatives.

Transcript

hello friends in this video we'll be discussing type two of calculus of variation that is function of higher order derivatives problem number one welcome back friends till now we are done with type 1 of calculus of variation now we are moving with the type 2 and type 2 is function of higher order derivatives for example see friends in now record th... Read More

Key Insights

• ✋ Type 2 of calculus of variation deals with problems containing higher order derivatives.
• ✋ The modified Euler's equation for type 2 calculus of variation includes terms for higher order derivatives.
• ⌛ Solving problems in type 2 calculus of variation often involves integrating the equation multiple times.
• 😑 The solution to a type 2 problem includes the dependent variable (Y) expressed in terms of the independent variable (X) and constants.
• 🪈 Functionals with higher order derivatives have a different form compared to functionals with first-order derivatives.
• ✋ Type 2 problems introduce more complexity and require consideration of higher order terms.
• 🍉 The modified Euler's equation for type 2 problems includes alternate plus-minus terms.

Questions & Answers

Q: What is the difference between type 1 and type 2 of calculus of variation?

Type 1 calculus of variation involves problems with only X, Y, and first-order derivatives, while type 2 includes higher order derivatives such as Y double dash, Y triple dash, etc.

Q: How does the Euler's equation change for type 2 calculus of variation?

The modified Euler's equation for type 2 calculus of variation includes terms for higher order derivatives, such as Y double dash, Y triple dash, etc., in addition to the first-order derivative.

Q: Can you provide an example problem that demonstrates type 2 calculus of variation?

The example problem in the video involves solving for Y in a functional equation that includes X, Y, and Y double dash.

Q: How is the solution to the problem obtained?

The solution involves integrating the equation multiple times, gradually reducing the number of derivatives until Y is obtained in terms of X and constants.

Summary & Key Takeaways

• The video introduces type 2 of calculus of variation, which deals with problems that include higher order derivatives.

• The Euler's equation for type 2 calculus of variation is modified to include higher order derivatives.

• The video solves a specific problem using the modified Euler's equation.