Cylindrical and spherical coordinates shalinishalini singh
In this Presentation, I have explained the co-ordinate system in three plain. ie Cylindrical, Spherical, Cartesian(Rectangular) along with its Differential formulas for length, area &volume.
Dealing with Notations and conventions in tensor analysis-Einstein's summation convention covariant and contravariant and mixed tensors-algebraic operations in tensor symmetric and skew symmetric tensors-tensor calculus-Christoffel symbols-kinematics in Riemann space-Riemann-Christoffel tensor.
Cylindrical and spherical coordinates shalinishalini singh
In this Presentation, I have explained the co-ordinate system in three plain. ie Cylindrical, Spherical, Cartesian(Rectangular) along with its Differential formulas for length, area &volume.
Dealing with Notations and conventions in tensor analysis-Einstein's summation convention covariant and contravariant and mixed tensors-algebraic operations in tensor symmetric and skew symmetric tensors-tensor calculus-Christoffel symbols-kinematics in Riemann space-Riemann-Christoffel tensor.
Lesson 6: Polar, Cylindrical, and Spherical coordinatesMatthew Leingang
"The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations.
A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined.
The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel.
Analytic Function, C-R equation, Harmonic function, laplace equation, Construction of analytic function, Critical point, Invariant point , Bilinear Transformation
Lesson 6: Polar, Cylindrical, and Spherical coordinatesMatthew Leingang
"The fact that space is three-dimensional is due to nature. The way we measure it is due to us." Cartesian coordinates are one familiar way to do that, but other coordinate systems exist which are more useful in other situations.
A vector has magnitude and direction. There is an algebra and geometry of vectors which makes addition, subtraction, and scaling well-defined.
The scalar or dot product of vectors measures the angle between them, in a way. It's useful to show if two vectors are perpendicular or parallel.
Analytic Function, C-R equation, Harmonic function, laplace equation, Construction of analytic function, Critical point, Invariant point , Bilinear Transformation
Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
Trigonometric Function of General Angles LectureFroyd Wess
More: www.PinoyBIX.org
Lesson Objectives
Trigonometric Functions of Angles
Trigonometric Function Values
Could find the Six Trigonometric Functions
Learn the signs of functions in different Quadrants
Could easily determine the signs of each Trigonometric Functions
Solve problems involving Quadrantal Angles
Find Coterminal Angles
Learn to solve using reference angle
Solve problems involving Trigonometric Functions of Common Angles
Solve problems involving Trigonometric Functions of Uncommon Angles
Comprehensive coverage of fundamentals of computer graphics.
3D Transformations
Reflections
3D Display methods
3D Object Representation
Polygon surfaces
Quadratic Surfaces
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
10. Converting between rectangular
and Cylindrical Coordinates
r
r
(r,,z)
cos( )
sin( )
x r
y r
z z
Rectangular to Cylindrical
2 2 2
tan( )
r x y
y
x
z z
Cylindrical to rectangularNo real surprises here!
11. Representing 3D points in Spherical
Coordinates
Spherical Coordinates are the 3D
analog of polar representations in
the plane.
We divide 3-dimensional space into
1. a set of concentric spheres centered at
the origin.
2. rays emanating outward from the origin
12. Representing 3D points in Spherical
Coordinates
(x,y,z)
We start with a point (x,y,z) given
in rectangular coordinates.
Then, measuring its distance
from the origin, we locate it on a
sphere of radius centered at the
origin.
Next, we have to find a way to
describe its location on the sphere.
13. Representing 3D points in Spherical
Coordinates
We use a method similar to the
method used to measure latitude
and longitude on the surface of the
Earth.
We find the great circle that goes
through the “north pole,” the “south
pole,” and the point.
14. Representing 3D points in Spherical
Coordinates
We measure the latitude or polar
angle starting at the “north pole” in
the plane given by the great circle.
This angle is called . The range
of this angle is
Note:
all angles are measured in
radians, as always.
0 .
15. Representing 3D points in Spherical
Coordinates
We use a method similar to the
method used to measure latitude
and longitude on the surface of the
Earth.
Next, we draw a horizontal circle
on the sphere that passes through
the point.
17. Representing 3D points in Spherical
Coordinates
We measure the latitude or azimuthal
angle on the latitude circle, starting at
the positive x-axis and rotating toward
the positive y-axis.
The range of the angle is
Angle is called .
0 2 .
Note that this is the same angle as the in cylindrical coordinates!
18. Finally, a Point in Spherical
Coordinates!
( , ,)
Our designated point on the
sphere is indicated by the three
spherical coordinates ( , , ) ---
(radial distance, azimuthal angle,
polar angle).
Please note that this notation is not
at all standard and varies from
author to author and discipline to
discipline. (In particular, physicists
often use to refer to the
azimuthal angle and refer to the
polar angle.)
19. Converting Between Rectangular
and Spherical Coordinates
(x,y,z)
z
r
First note that if r is the usual cylindrical
coordinate for (x,y,z)
we have a right triangle with
•acute angle ,
•hypotenuse , and
•legs r and z.
It follows that
sin( ) cos( ) tan( )
r z r
z
What happens if
is not acute?
20. Converting Between Rectangular
and Spherical Coordinates
(x,y,z)
z
r
cos( ) sin( )cos( )
sin( ) sin( )sin( )
cos( )
x r
y r
z
Spherical to rectangular
21. Converting from Spherical to
Rectangular Coordinates
(x,y,z)
z
r
Rectangular to Spherical
2 2 2
2 2
2 2 2
tan( )
tan( )
cos( )
x y z
y
x
x yr
z z
z z
x y z
23. Integration Elements:
Rectangular Coordinates
We know that in a Riemann Sum approximation for a
triple integral, a summand
This computes the function value at some point in the little
“sub-cube” and multiplies it by the volume of the little
cube of length , width , and height .
* * *
( , , ) .i i i i i if x y z x y z
* * *
function value volume of the small
at a sampling point cube
( , , ) .i i i i i if x y z x y z
1 4 2 4 3 14 2 43
ix iy iz
24. Integration Elements:
Cylindrical Coordinates
What happens when we consider small changes
in the cylindrical coordinates r, , and z?
, , andr z
We no longer get a
cube, and (similarly to
the 2D case with polar
coordinates) this affects
integration.
25. Integration Elements:
Cylindrical Coordinates
What happens when we consider small changes
in the cylindrical coordinates r, , and z?
, , andr z
Start with our previous
picture of cylindrical
coordinates:
r
r
26. Integration Elements:
Cylindrical Coordinates
What happens when we consider small changes
in the cylindrical coordinates r, , and z?
, , andr z
Start with our previous
picture of cylindrical
coordinates:
Expand the radius by a
small amount:
r
r
r+r
r
32. Integration in Cylindrical Coordinates.
dA r dr d
We need to find the volume of this little solid.
As in polar coordinates, we have the area of a horizontal
cross section is. . .
33. Integration in Cylindrical Coordinates.
dV r dr d dz
We need to find the volume of this little solid.
Since the volume is just the base times the height. . .
So . . .
( , , )
S
f r z r dr d dz