User:Egm6341.s10.Team4.nimaa&m/HW6

From Wikiversity
Jump to: navigation, search

Problem 2: Rate of momentum change for optimal control problem[edit]

Given[edit]

Envisage the below figure as free body diagram of an aircraft:

HW-6.2-1.jpg.

likewise consider the shown axes and vectors, for at :

HW-6.2.3.jpg.

Find[edit]

Show that .

Solution[edit]

According to the above figure, we can survey these two cases at and , the velocity of the aircraft after will reach to and the angle between the aircraft and horizontal axis will reach to the . Thus, regarding generated angle between two velocity vectors, we can write:

The amount of can be neglected in front of .

On the other hand, momentum is defined as . So, we have:

Assuming the amount of to be negligible in front of changes in velocity;

Finally, we can summarize the answer as:

.



Author[edit]

Solved and typed by - Egm6341.s10.Team4.nimaa&m 03:08, 3 April 2010 (UTC) .




Problem 7: Expression for Hermitian interpolation at [edit]

Given[edit]

Consider the Hermitian interpolation by the following equation (on slide 35-2):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Expected width > 0."): {\displaystyle \displaystyle }

Find[edit]

Show the following expression can be obtained for :

Solution[edit]

By differentiating from the equation for , we will attain:

Now, we can compute the followings:

The acquired foregoing equation is equal to RHS of the expression. Now, we can compute the LHS of it as:

.

Author[edit]

Solved and typed by - Egm6341.s10.Team4.nimaa&m 04:15, 3 April 2010 (UTC) .




Problem 8: Expression for derivative of Hermitian interpolation at [edit]

Given[edit]

Consider the Hermitian interpolation by the following equation (on slide 35-2):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Expected width > 0."): {\displaystyle \displaystyle }

Find[edit]

Show the following expression can be obtained for :

Solution[edit]

By differentiating from the equation for , we will attain:

Now, we can compute the followings:

The acquired foregoing equation is equal to RHS of the expression. Now, we can compute the LHS of it as:


.

Author[edit]

Solved and typed by - Egm6341.s10.Team4.nimaa&m 04:23, 3 April 2010 (UTC) .