Lesson 16 The Essence of Lagrangian Dynamics, Conservation Theorems
1) It's time again to try to make some brain connections and to look at things from a "big picture perspective." Our textbook suggests that the Lagrangian and Newtonian formulations of mechanics are equivalent. We'll be discussing this in class.
What is it that we are basically trying to do with the Lagrangian formulation? (That is, what's the goal of all this Lagrangian stuff?)
How about with the Newtonian formulation?
In your own words, briefly explain/describe how you think the two formulations are equivalent.
2) The Lagrangian for Comet Hale-Bopp is rotationally invariant. (What does that mean?!)
Hale-Bopp's orbital period around the Sun this last time was about 4200 years. When it made its closest approach to the Sun on 1 April 1997, it was about .85 AU (1 AU = 1 Astronomical Unit = Earth to Sun distance = 1.5 x 1011m) from the Sun and was traveling at about 44 km/s. At its farthest from the Sun, it is about 372 AU away. Use the fact that the Lagrangian is rotationally invariant to estimate about how fast Hale-Bopp travels through space when it is farthest from the Sun.
3) Which set of words will result in making the best statement?
"Newtonian formulation" is to ______________ as "Lagrangian formulation" is to ________________.
[Note: Feel free to briefly justify your choice in the 'Comments box' below.]
You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.
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