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# Involving Hamiltonian Dynamics

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Involving Hamiltonian Dynamics
problem 5.6

A mass m is suspended by a massless spring of spring constant k and unstretched length b. The suspension point has a constant upward acceleration a(0 subscript of a). Gravity is acting vertically downward. Find the Lagrangian and Hamiltonian functions and obtain Hamilton's equations of motion. What is the period of motion?

Problem involving the Poisson Brackets
5.16
Determine the Poisson brackets formed from the Cartesian components of the momentum p and the angular momentum
L = r * p. HINT( * IS THE MULTIPLICATION SYMBOL)

Problem 4.5 comes from The Lagrangian Formulation of Mechanics section
4.5
Three uniform rods AB,BC,CD, each of mass m and length 2b, are smoothly hinged at B and C. This system is suspended from end A. A horizontal force F is applied at the other end, D. Find the equilibrium configuration.

https://brainmass.com/physics/periodic-motion/involving-hamiltonian-dynamics-147048

#### Solution Preview

5.6
We assume that the system is 1-dimensional and address it in the frame moving together with the suspension point, so that we replace the free fall acceleration g by (g+a) and write the quasi-gravitational potential energy as

-m(g+a)y

where the vertical coordinate is counted from the suspension point DOWNWARDS.

The potential energy of the spring is k(y-b)^2/2 and the kinetic energy of the mass is m(dy/dt)^2/2, so that the Lagrangian
is

L = m(dy/dt)^2/2 - k(y-b)^2/2 + m(g+a)y =

= m(dy/dt)^2/2 - k(y-q)^2/2 + const,

where

q = b + m(g+a)/k

and the constant is unimportant so that we shall drop the constant hereafter.

The momemtum is

p = mdy/dt,

the Hamiltonian is

H = p^2/(2m) ...

#### Solution Summary

A mass m is suspended by a massless spring of spring constant k and unstretched length b. The suspension point has a constant upward acceleration a(0 subscript of a). Gravity is acting vertically downward. Find the Lagrangian and Hamiltonian functions and obtain Hamilton's equations of motion. What is the period of motion?

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## Understanding the dynamics of competition and the major players

I really need some serious help getting started with this massive project! Thank you so much.

Assignment One:
Summarize in three pages, one of the ten schools from book: Strategy Safari: A Guided Tour Through The Wilds of Strategic Management by Henry Mintzberg, Joseph Lampel and Bruce Ahlstrand; what I need is to Summarize in three pages, one of the ten schools, for example read and summarize "the Design School" in 3 pages.
P.S: If you do not have access to the book, you can have it online by Google it. Be sure that the paper submitted for this assignment is APA styled, 6th ED. And formatted, including all references. Cite inside the paper and show it on the references page. Please 3 pages

Book: Strategy Safari: A Guided Tour Through The Wilds of Strategic Management by Henry Mintzberg, Joseph Lampel and Bruce Ahlstrand;
ISBN10: 0684847434
ISBN13: 9780684847436

Assignment Two:
Understanding the dynamics of competition and the major players, Understanding the competition in the Alternative Energy Industries (AEI) is important. This assignment requires each individual team member to develop an analysis of one of the key AEI. Be sure that the paper submitted for this assignment is APA styled and formatted, including all references. At minimum, your 3 page analysis must include the following:
? Who are the major industry players?
? Develop a Snapshot of each by analyzing the current performance (financials and other key metrics such as units sold by category, units in the pipeline/inventory, and other factors determined through your research).
? Examine what each "giant" is doing to enter new markets, either with new product offerings or new geographic markets,
? Determine how it is entering new markets (i.e. mergers and acquisitions, internal growth, joint ventures).

P.S: Some Alternative Energy Industry (AEI) Links.
http://www.claiborneconferencecenter.org/control-of-energy/major-industry-players/
http://www.zacks.com/stock/news/48670/Alternative+Energy+Industry+Outlook+%96+March+2011

Assignment Three:
1. Understanding the Importance of Firm Resources-as a source of sustainable competitive advantage and for competing on the basis of capabilities to achieve sustainable competitive advantage.
This week's written individual and team assignments are intended to explore the myriad topics that enter into analyzing a firm's resources, its ability to innovate and, also, to discern what and how Value Innovation occurs.

? What are Industry Profit Pools? Individually (I), in a 3 page paper, determine where pools exist in the Alternative Energy Industries AEI. Defend your position with research and create an industry profit pool map. Be sure that the paper submitted for this assignment is APA 6th. ED styled and formatted, including all references.

2. Values Innovation: As a team (T), research the topic of Value Innovation. In a 3 page paper:
? Apply this idea to the Alternative Energy Industries (AEI) (industry) with special attention to the opportunity in all sectors (winds, solar and nuclear).
P.S: one page for winds, one page for Solar; and one page for nuclear.
Be sure that the paper submitted for this assignment is APA 6th. ED styled and formatted, including all references.

3. Discussion Assignment: Individually, now that you're half-way through the course, what have you learned about strategic planning that you did not know before? In what ways have you deepened your knowledge of strategic planning and implementation? In what ways has the SFL 5-step process assisted your work on the assignments completed thus far? In what ways can the SFL process assist you in completing the final team project?

** Please open the Student SFL Guide as well! **

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