Typically, the orientation is given relative to a frame of reference, usually specified by a Cartesian coordinate system.Two objects sharing the same direction are said to be codirectional (as in parallel lines).Two directions are said to be opposite if they are the additive inverse of one another, as in an arbitrary unit vector and its multiplication by -1.Two directions are obtuse if they form an obtuse angle (greater than a right angle) or, equivalently, if their scalar product or scalar projection is negative.

In general the position and orientation in space of a rigid body are defined as the position and orientation, relative to the main reference frame, of another reference frame, which is fixed relative to the body, and hence translates and rotates with it (the body's local reference frame, or local coordinate system). At least three independent values are needed to describe the orientation of this local frame. Three other values describe the position of a point on the object.All the points of the body change their position during a rotation except for those lying on the rotation axis. If the rigid body has rotational symmetry not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the Earth, often described using the orientation of a line joining it with the Earth's center, measured using the two angles of longitude and latitude. Likewise, the orientation of a plane can be described with two values as well, for instance by specifying the orientation of a line normal to that plane, or by using the strike and dip angles.


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In two dimensions the orientation of any object (line, vector, or plane figure) is given by a single value: the angle through which it has rotated. There is only one degree of freedom and only one fixed point about which the rotation takes place.

The first attempt to represent an orientation is attributed to Leonhard Euler. He imagined three reference frames that could rotate one around the other, and realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space (using two rotations to fix the vertical axis and another to fix the other two axes). The values of these three rotations are called Euler angles.

These are three angles, also known as yaw, pitch and roll, Navigation angles and Cardan angles. Mathematically they constitute a set of six possibilities inside the twelve possible sets of Euler angles, the ordering being the one best used for describing the orientation of a vehicle such as an airplane. In aerospace engineering they are usually referred to as Euler angles.

Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle. Therefore, any orientation can be represented by a rotation vector (also called Euler vector) that leads to it from the reference frame. When used to represent an orientation, the rotation vector is commonly called orientation vector, or attitude vector.

With the introduction of matrices, the Euler theorems were rewritten. The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix.

The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real eigenvalue). The product of two rotation matrices is the composition of rotations. Therefore, as before, the orientation can be given as the rotation from the initial frame to achieve the frame that we want to describe.

The configuration space of a non-symmetrical object in n-dimensional space is SO(nRn. Orientation may be visualized by attaching a basis of tangent vectors to an object. The direction in which each vector points determines its orientation.

Another way to describe rotations is using rotation quaternions, also called versors. They are equivalent to rotation matrices and rotation vectors. With respect to rotation vectors, they can be more easily converted to and from matrices. When used to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions.

The attitude of a lattice plane is the orientation of the line normal to the plane,[2] and is described by the plane's Miller indices. In three-space a family of planes (a series of parallel planes) can be denoted by its Miller indices (hkl),[3][4] so the family of planes has an attitude common to all its constituent planes.

The attitude of a rigid body is its orientation as described, for example, by the orientation of a frame fixed in the body relative to a fixed reference frame. The attitude is described by attitude coordinates, and consists of at least three coordinates.[6] One scheme for orienting a rigid body is based upon body-axes rotation; successive rotations three times about the axes of the body's fixed reference frame, thereby establishing the body's Euler angles.[7][8] Another is based upon roll, pitch and yaw,[9] although these terms also refer to incremental deviations from the nominal attitude

Our Week of Welcome is a required orientation experience designed to help you build connections at CWU. You will have the opportunity to familiarize yourself with campus, connect with other students, develop wellness strategies, and learn about procedures, expectations, and contributing to the community. We want to help prepare you for a successful academic experience and in addition to many fun activities, there will be several educational sessions and workshops to kick off your journey. Learn more about Week of Welcome.

Submit your SIR today! Register for your orientation session to start your journey at UC Merced. After registering, you can check out the Pre-Orientation Checklist. Please ensure you also complete your online pre-orientation two weeks prior to your scheduled orientation.

This program will help you make a successful transition to UNLV! Attending orientation is mandatory for all first-year students. All first-year students must also complete the Online Pre-Orientation course in WebCampus before attending their scheduled orientation.

First-year students will receive their class schedules during orientation and learn valuable information about degree requirements. Guests are not permitted to attend advising and class registration sessions with their students.

Your academic advisor will enroll you in the appropriate courses based on your major and official placement information submitted to the Office of Admissions. If you do not have official placement scores or wish to improve your placement, review the UNLV Placement Assessment options. Official placement information must be submitted to the Office of Admissions prior to your scheduled orientation.


As a new student, you are required to attend our in-person orientation before your classes begin.Remember to reserve your spot in advance by completing our Intent to Enroll Form.

Dates and schedules for upcoming orientations are below: Winter 2024: December 27 - December 29, 2023 Spring 2024: March 25 - March 29, 2024 Summer 2024: June 17 - June 21, 2024 Fall 2024: September 16 - September 20, 2024Checking in online and attending our in-person orientation are mandatory for all new students. Checking in online is necessary to maintain your immigration status. Students who are unable to attend orientation and report to their campus IP office by the first day of class may need to defer their enrollment to a future quarter. Contact IntlFutureStudent@seattlecolleges.edu for further guidance.

In addition to attending orientation, you are encouraged to connect with us via Facebook. Approximately 1-2 months before the start of your first quarter, you will receive an email inviting you to join a private Facebook group for new international students at Seattle Colleges. The purpose of the group is to allow you to connect with fellow schoolmates, ask questions, and get answers as you prepare to enroll. We will send the invitation to the email address listed on your admission application -- so keep an eye out! To join our private group, follow the instructions included in the email message.

The following video covers the roles, duties, and responsibilities of a guardian and what to expect if you are appointed as a guardian of the person or property. Prospective guardians must watch the entire video before appointment as guardian of a disabled person or minor. The orientation and training requirements do not apply to public guardians or guardianships that terminate parental rights.

By choosing to attend college, you are investing your time and your money. The time you spend in our online orientation system will help you maximize your investment and help you be in control of your educational future.

To access the system, log in to the myEFSC Portal using your student email address and password and look for the Student Orientation/Titan Preview icon. Clicking that button once logged in to the myEFSC Portal will begin the orientation. If you cannot complete the process at one sitting, the system will remember where you left off and pick up there when you log back in through myEFSC.

If you have been conditionally accepted into a program that requires a special limited access application, such as health sciences and nursing, or in the public safety field, you may be required to take part in an additional orientation for your specific program. For those limited access programs, the main college orientation is still required for first-time EFSC students. ff782bc1db

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