DOC PREVIEW
MSU ME 371 - LECTURE NOTES

This preview shows page 1-2-3-4-5 out of 16 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 16 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

PowerPoint PresentationHomework ProblemsSlide 3Slide 43-D Vectors; Base Vectors3-D Rectangular CoordinatesWriting 3-D Components3-D Direction CosinesUnit Base VectorsVector Equality in ComponentsAdditional Vector OperationsGeneral Unit VectorsPosition Vectors in SpaceVectors in Matrix FormSummaryExample ProblemME 221 Lecture 4 1ME 221 StaticsLecture #4Sections 2.4 – 2.5ME 221 Lecture 4 2Homework Problems•Due Today:–1.1, 1.3, 1.4, 1.6, 1.7–2.1, 2.2, 2.11, 2.15, 2.21•Due Wednesday, September 9:–Chapt 2: 22, 23, 25, 27, 29, 32, 37, 45, 47 & 50–On 2.50:•Solve with hand calculations first•Then use MathCAD, MatLab, Excel, etc. to solve•Quiz #1 – Friday, 9/5ME 221 Lecture 4 3TA Hours• Help Sessions – ME Help Room – 1522EB - Cubicle #2 • TA’s: – Jimmy Issa, Nanda Methil-Sudhakaran & Steve RundellMondays & Wednesdays – 10:15am to 5:00pmTuesdays & Thursdays – 8:00am to 5:00pmFridays – 8:00am to 11:00am• Grader – Jagadish Gattu2415EB – Weds: 10:00am to 12:00amME 221 Lecture 4 4Last Lecture•Vector Components• Scalar Multiplication of Vectors• Perpendicular Vectors• Example 2.3ME 221 Lecture 4 53-D Vectors; Base Vectors•Rectangular Cartesian coordinates (3-D)•Unit base vectors (2-D and 3-D)•Arbitrary unit vectors•Example problem•Vector component manipulationME 221 Lecture 4 63-D Rectangular Coordinates•Coordinate axes are defined by OxyzxyzOCoordinates can be rotatedany way we like, but ...•Coordinate axes must be a right-handed coordinate system.ME 221 Lecture 4 7xyzOA =Writing 3-D Components•Component vectors add to give the vector:xyzOA=AxAx +AyAy +AzAzAlso,2x  2 2y zA A A AME 221 Lecture 4 83-D Direction CosinesThe angle between the vector and coordinate axis measured in the plane of the twoxyzOAxcosx x  xAAycosyy y  AAzcoszz z  AAWhere: x2+y2+z2=1ME 221 Lecture 4 9Unit Base VectorsAssociate with each coordinate, x, y, and z, a unit vector (“hat”). All component calculations use the unit base vectors as grouping vectors.xyzOˆˆjˆkNow write vector as follows:ˆˆˆx y zA A j A k  Awhere Ax = |Ax|Ay = |Ay|Az = |Az|ME 221 Lecture 4 10Vector Equality in Components•Two vectors are equal if they have equal components when referred to the same reference frame. That is:ˆ ˆˆ ˆˆ ˆx y z x y zA A j A k B B j B k     ifAx = Bx , Ay = By , Az = BzME 221 Lecture 4 11Additional Vector Operations•To add vectors, simply group base vectors      ˆ ˆˆ ˆˆ ˆˆˆˆx y z x y zx x y y z zA A j A k B B j B kA B A B j A B k          •A scalar times vector A simply scales all the components ˆ ˆˆ ˆˆ ˆx y z x y zA A j A k A A j A k         ME 221 Lecture 4 12General Unit Vectors•Any vector divided by its magnitude forms a unit vector in the direction of the vector.–Again we use “hats” to designate unit vectorˆˆˆˆyxzbbbj k   bbb b b bxyzObˆbME 221 Lecture 4 13Position Vectors in Space•Points A and B in space are referred to in terms of their position vectors.xyzOrAˆˆˆA A A Ax y j z k  rrBˆˆˆB B B Bx y j z k  rrB/A     /ˆˆˆB BA AB A B Aj z ky zx x y     r•Relative position defined by the differenceME 221 Lecture 4 14Vectors in Matrix Form•When using MathCAD or setting up a system of equations, we will write vectors in a matrix form:ˆˆˆxx y z yzAA A j A k AA        AME 221 Lecture 4 15Summary•Write vector components in terms of base vectors•Know how to generate a 3-D unit vector from any given vectorME 221 Lecture 4 16Example


View Full Document

MSU ME 371 - LECTURE NOTES

Download LECTURE NOTES
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view LECTURE NOTES and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view LECTURE NOTES 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?