User:Egm6321.f11.team3.chang

From Wikiversity
Jump to navigation Jump to search


Problem1. Second total time derivative[edit]


Given[edit]


From lecture note 2-4, first total time derivative is given by,


with



Find[edit]

Show that


with


Similarly for the other partial derivatives

Solution[edit]

Let



Problem 2: Deriving 1st and 2nd Total Time Derivatives; Demonstrate Similarity to Coriolis Force Derivation[edit]


Given[edit]


The equation of motion (EOM) for the maglev train is modeled by:


From lecture notes on page 2-4, the 1st total time derivative is given by:

(Eq.2A)


and the 2nd total time derivative, on page 2-5, is given by:

(Eq.2B)


Problem[edit]


--Derive the 1st total time derivative.
--Derive the 2nd total time derivative.
--Show the similarity with the derivation of the Coriolis force.

Solution, First Total Time Derivative[edit]


Applying the chain rule to


Yields:



Since:




Then the equation can be rewritten as:


And simplified to return to equation 2A:


Solution, Second Total Time Derivative[edit]


Coriolis Force Derivation Similarity[edit]



Problem3.[edit]

Given[edit]

Find[edit]

Solution[edit]

Problem4.[edit]

Given[edit]

ξ = (ξ123)
X(ξ) = X11)X22)X33)

(5.1)

Find[edit]

Solution[edit]

Problem5.[edit]

Given[edit]

Find[edit]

Show that:


Becomes:

Solution[edit]

Problem6.[edit]

Given[edit]

Find[edit]

Show \ is nonlinear with respect to .

Solution[edit]

Problem7.[edit]

Given[edit]

Find[edit]

Show that : is linear

Solution[edit]

Let u(x) and v(x) be any 2 functions of x Let : be and 2 real numbers We write :

So it is linear.


Problem8.[edit]

Given[edit]

Find[edit]

Find the integration constants in terms of the initial conditions :

Solution[edit]




Contributing Members & Referenced Lecture (Placeholder)[edit]

Team Contribution Table
Problem Number Assigned To Solved By Proofread By
1.1 YungSheng Chang YungSheng Chang
1.2 Joel Brawner
1.3 Gopichandran Prashant
1.4 Gopichandran Prashant YungSheng Chang
1.5 Anderson Robert and Sahin Ismail Hakki
1.6 Anderson Robert
1.7 Chao Yang Chao Yang
1.8 Chao Yang Chao Yang