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Conceptual basis of classical mechanics
Published in Bijan Kumar Bagchi, Advanced Classical Mechanics, 2017
Newton’s first law also defines a class of reference frames which are called inertial frames. These reference frames are not supposed to undergo any type of acceleration. In other words, an inertial frame moves with a constant velocity or is at rest with respect to any other inertial frame. In 1886 Ludwig Lange, a German physicist, defined an inertial frame to be: “A reference frame in which a mass point thrown from the same point in three different noncoplanar directions follows rectilinear paths each time it is thrown, is called an inertial frame.” An inertial frame may be looked upon as the one that is fixed relative to the average position of a fixed star or that is moving with a constant velocity and without any rotation relative to it. According to Newton, absolute space and time form a convenient background against which we visualize occurrence of physical phenomena but the background itself cannot be influenced by physical events themselves. To describe a physical event, a fixed reference coordinate frame (inertial) must be chosen with respect to which the location of a material object is defined.
Review of Conceptual Models of Estimating the Spatio-Temporal Variations of Water Depth Using Remote Sensing and GIS for the Management of Dams and Reservoirs
Published in Shruti Kanga, Suraj Kumar Singh, Gowhar Meraj, Majid Farooq, Geospatial Modeling for Environmental Management, 2022
Absolute space is the mathematical space, the determination of which involves the precise measurement of location and space, such as an X, Y, and Z coordinate. These coordinates provide an unambiguous description of the space.
General Ideas of Natural Science, Signal Theory, and Information Theory
Published in Andrey Popoff, Fundamentals of Signal Processing in Metric Spaces with Lattice Properties, 2017
During the development of natural sciences and philosophy of New Time, teaching about space became inseparably linked with principles of mechanics developed by Isaac Newton and Galileo Galilei. Newton put forth the notions of absolute space and relative space into the base of his mechanics. Within contemporary interpretation, Newton’s theses on classical mechanics [194] state:Space exists independently of anything in the world.Space contains all the objects of nature and gives the place to all of its phenomena, but does not experience their influence upon itself.Space is everywhere and the same with respect to its properties. All its points are equitable and the same — space is isotropic.In all times space is invariably the same.Space is ranging along all the directions unrestrictedly and has infinite volume.Space has three dimensions.Space is described by Euclidean geometry.Newton’s understanding was considered the only true one for almost two centuries despite Gottfried Leibniz’ opposing position [195]. Leibniz detected a boundedness of Newton’s overview of space and considered the separation of space from matter to be erroneous. He wrote, “What is the space without a material object? ...Unhesitatingly I will answer that I do not know anything about this.” Leibniz considered space as a property of the world of material objects without which it could not exist. This interpretation of the notion of space, while logical, did not correspond to the majority opinion about the unity and universality of Euclidean geometry. Although Leibniz’s idea seemed incontestable and obvious, the scientific community would not even discuss the possible existence of a geometry other than Euclidean.
Trunk and shoulder kinematics of rowing displayed by Olympic athletes
Published in Sports Biomechanics, 2023
Yumeng Li, Rachel M. Koldenhoven, Nigel C. Jiwan, Jieyun Zhan, Ting Liu
The test protocol of this study was approved by the institutional review board of Texas State University. Informed consent was obtained from the participants before data collection. Seven inertial measurement units (IMU, MyoMotion Research PRO, Noraxon USA Inc., Scottsdale, AZ, USA) were placed and secured by straps on participants’ pelvis, lumbar spine, thoracic spine, scapula and upper arms. The IMU sensors included a three-dimensional accelerometer, gyroscope, and magnetometer that could be used to track the angular orientation of body segments in absolute space. Previous research has demonstrated satisfactory measurement reliability and validity of the IMU system (Yoon, 2017). IMU placement was based on the manufacturer’s recommendation to ensure an accurate calibration. The IMU for the pelvis was placed on the sacrum. The lumbar spine IMU was placed on the 3rd lumbar vertebra. The thoracic spine IMU was placed on the 2nd thoracic vertebra. The scapula IMU was placed on the centre of the scapula. The upper arm IMUs were placed bilaterally on the midway between the shoulder and elbow joints, lateral to the humerus. The IMUs of all participants were placed by the same investigator to ensure consistency. Participants were instructed to stand still on both feet and remain stationary for 20 seconds to calibrate the neutral position. The arms were kept relaxed at the sides and the palms were aligned with the sagittal plane. During the calibration process, investigators kept as quiet as possible to minimise environmental distraction for the participants.
Towards the next-generation GIS: a geometric algebra approach
Published in Annals of GIS, 2019
Linwang Yuan, Zhaoyuan Yu, Wen Luo
Non-Euclidean geometry expands the mathematical and physical space from absolute to relative parameters. This lays the mathematical foundation for the change from Newton’s absolute space view (Euclidean space) to Einstein’s relativistic space view (Minkowski space and Riemannian space). GA is as an important breakthrough in the development of non-Euclidean geometry, which is a unified description language used to link geometry and algebra, mathematics and physics, and ultimately achieve the unified expression of Euclidean, Minkowski and Riemann spaces. GA, as the name implies, is characterized by representing, constructing and manipulating geometric objects with an algebraic language. Various geometric systems (such as projective geometry, affine geometry, conformal geometry, differential geometry, etc.) and algebraic systems (such as calculus, tensor algebra, Boolean algebra, space-time algebra, etc.) can be mapped to GA spaces (Figure 1). Therefore, GA can be used to build an unified framework of geography and space-time, for innovatively constructing unified multidimensional representations, and develop analysis and modelling methods in GIS. It is also compatible with the data models, computational and analytical methods of a more general GIS based on mathematical theory.