Introduction to Statics and Dynamics P2 doc

... of two vectors 23 2.2 The dot product of two vectors The dot product is used to project a vector in a given direction, to reduce a vector to components, to reduce vector equations to scalar equations, ... vector can be broken down into a sum of components each parallel to one of the orthogonal base vectors. Another useful decomposition is this: Given any vector  A and a unit ve...

Ngày tải lên: 25/01/2014, 15:20

... two vectors The dot product is used to project a vector in a given direction, to reduce a vector to components, to reduce vector equations to scalar equations, to define work and power, and to help ... generalize to this: the tendency of a force to cause rotation is proportional to the size of the force and to its distance from the hinge (for forces perpendicular t...

Ngày tải lên: 03/07/2014, 12:20

... distinguishing vectors from scalars. Vector addition is motivated by the need to add forces and relative positions, dot products are motivated as the tool which reduces vector equations to scalar equations, and ... expands statics to include material properties and also pays more attention todistributed forces (traction and stress). This book only occasionally touches lightly...

Ngày tải lên: 25/01/2014, 15:20

... of two vectors 23 2.2 The dot product of two vectors The dot product is used to project a vector in a given direction, to reduce a vector to components, to reduce vector equations to scalar equations, ... distinguishing vectors from scalars. Vector addition is motivated by the need to add forces and relative positions, dot products are motivated as the tool which reduces vector...

Ngày tải lên: 12/03/2014, 18:23

... main mathematical tool here is the vector cross product, a second way of multiplying vectors together. The cross product is used to define (and calculate) moment and to calculate various quantities in dynamics. ... how to think about it your own way, to become an expert in your own style, and to do the work in the way that makes things most clear to you and your readers. Wh...

Ngày tải lên: 08/04/2014, 11:26

... ABCand D are constants and λ = √ k/m. We need initial conditions to evaluate the constants ABCand D. Since the mass starts at t = 0 from the rest position when θ = θ o , x(0) =− cos θ o and ... calculator using trial and error. Here is a M ATLAB script which finds t f and plots the path of the collar from t = 0stot = t f : tf = fzero(’slidebar’,2); % run built-in function fzero % t...

Ngày tải lên: 08/04/2014, 11:26

... after 1 4 , 1 2 , 3 4 , and 1 revolution. Draw the velocity vector (by hand) on your plot. Draw the direction accu- rately and draw the lengths of the vec- tors in proportion to their magnitude. You ... length of the shaft is 2d. A motor applies a torque M motor along theaxisof the shaft. Attheinstant shown in the figure, assume m, , d, ω and M motor are known and the rod lies in th...

Ngày tải lên: 08/04/2014, 11:27

... machines and machine parts are designed to move something. Bicycles, planes, elevators, and hearses aredesigned to move people; a clockwork, to moveclock hands; insect wings, to move insect bodies; and ... tools: • A vector calculator that always keeps vectors and scalars distinct, and • A reliable and clear free body diagram drawing tool. Because manyof the terms in mecha...

Ngày tải lên: 03/07/2014, 12:20

... dot product is used to project a vector in a given direction, to reduce a vector to components, to reduce vector equations to scalar equations, to define work and power, and to help solve geometry ... tools: • A vector calculator that always keeps vectors and scalars distinct, and • A reliable and clear free body diagram drawing tool. Because manyof the terms in mechani...

Ngày tải lên: 17/03/2014, 14:24

... Introduction to Preinstalling and Deploying Microsoft Windows 2000 Professional 9 Business Problem To keep up with customer demand, OEM system builders and organizations must be able to ... Introduction to Preinstalling and Deploying Microsoft Windows 2000 Professional 5 Business Problem To keep up with customer demand, OEM system builders and organizations m...

Ngày tải lên: 10/12/2013, 16:15