Lecture

Kinematics: Curvilinear Abscissa

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Description

This lecture covers the concept of curvilinear abscissa in kinematics, discussing the choice of positive direction, generalization, and comparison of durations. It also explains the origin selection and the use of tangent vectors to indicate the chosen positive direction.

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Related concepts (31)

Kinematics

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.

Inverse kinematics

In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics.

Robot kinematics

In robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques.

Greek alphabet

The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BC, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today.

Greek diacritics

Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography (πολυτονικό σύστημα γραφής), which includes five diacritics, notates Ancient Greek phonology. The simpler monotonic orthography (μονοτονικό σύστημα γραφής), introduced in 1982, corresponds to Modern Greek phonology, and requires only two diacritics. Polytonic orthography () is the standard system for Ancient Greek and Medieval Greek.

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