Dr. Friedrich FUTSCHIK: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=8495
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 02 Dec 2021 12:08:25 GMTThu, 02 Dec 2021 12:08:25 GMTNew applications published by Dr. Friedrich FUTSCHIKhttps://www.maplesoft.com/images/Application_center_hp.jpgDr. Friedrich FUTSCHIK: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=8495
Dynamics on Our Rotating Earth
https://www.maplesoft.com/applications/view.aspx?SID=1650&ref=Feed
The general relationship between two rotating coordinate systems has been established and the behaviour of moving objects in the vicinity of the rotating earth's surface has been analysed. Amongst others, a mathematical analysis of the historical demonstration of the earth's rotation with his pendulum by Foucault, 1850 in the pantheon in Paris is presented.<img src="https://www.maplesoft.com/view.aspx?si=1650/Freier_Fall_88.gif" alt="Dynamics on Our Rotating Earth" style="max-width: 25%;" align="left"/>The general relationship between two rotating coordinate systems has been established and the behaviour of moving objects in the vicinity of the rotating earth's surface has been analysed. Amongst others, a mathematical analysis of the historical demonstration of the earth's rotation with his pendulum by Foucault, 1850 in the pantheon in Paris is presented.https://www.maplesoft.com/applications/view.aspx?SID=1650&ref=FeedMon, 08 Aug 2005 04:00:00 ZDr. Friedrich FUTSCHIKDr. Friedrich FUTSCHIKKinematics of Our Earth-Moon System
https://www.maplesoft.com/applications/view.aspx?SID=1501&ref=Feed
Apart from Newtonian forces of attraction between masses and Einstein's theory of gravitation, we can get an insight into the movements of our moon by using Maple's Linear Algebra Package and some key data about our only natural satellite.<img src="https://www.maplesoft.com/view.aspx?si=1501/EarthMoon.gif" alt="Kinematics of Our Earth-Moon System" style="max-width: 25%;" align="left"/>Apart from Newtonian forces of attraction between masses and Einstein's theory of gravitation, we can get an insight into the movements of our moon by using Maple's Linear Algebra Package and some key data about our only natural satellite.https://www.maplesoft.com/applications/view.aspx?SID=1501&ref=FeedWed, 25 May 2005 00:00:00 ZDr. Friedrich FUTSCHIKDr. Friedrich FUTSCHIKAccelerated Motion in Special Relativity
https://www.maplesoft.com/applications/view.aspx?SID=1469&ref=Feed
Usually, the content of the theory of special relativity is reduced to the description of uniform motion and the corresponding Lorentz Transformations. The pure geometrical interpretation of the theory is attributed to the theory of general relativity with its assumptions concerning general coordinate transformations. That this is not a correct opinion will be shown.
Both theories are theories of a space-time world and admit arbitrary permissible coordinate transformations. In a sense, "general relativity" is not a good name for the theory, the main meaning of which is the interpretation of gravitation as a curvature of space-time. The difference between the two theories concerns the space-time structure: the flat, pseudo-Euclidian (topologically simple) manifold of special relativity and the curved, Riemannian (topologically nontrivial) manifold of the general relativity.
The gravitation is the curvature and, as a result of its tensor nature, we cannot "turn it off" in some finite region by means of a coordinate transformation.
Therefor, the equivalence principle has only a local and heuristic meaning. An observer can always distinguish gravitation from acceleration. It should be emphasized that the acceleration is not allied to the curvature of space-time and, as a result, it can be described in the framework of the special relativity.<img src="https://www.maplesoft.com/view.aspx?si=1469/Clock_Paradox_136.gif" alt="Accelerated Motion in Special Relativity" style="max-width: 25%;" align="left"/>Usually, the content of the theory of special relativity is reduced to the description of uniform motion and the corresponding Lorentz Transformations. The pure geometrical interpretation of the theory is attributed to the theory of general relativity with its assumptions concerning general coordinate transformations. That this is not a correct opinion will be shown.
Both theories are theories of a space-time world and admit arbitrary permissible coordinate transformations. In a sense, "general relativity" is not a good name for the theory, the main meaning of which is the interpretation of gravitation as a curvature of space-time. The difference between the two theories concerns the space-time structure: the flat, pseudo-Euclidian (topologically simple) manifold of special relativity and the curved, Riemannian (topologically nontrivial) manifold of the general relativity.
The gravitation is the curvature and, as a result of its tensor nature, we cannot "turn it off" in some finite region by means of a coordinate transformation.
Therefor, the equivalence principle has only a local and heuristic meaning. An observer can always distinguish gravitation from acceleration. It should be emphasized that the acceleration is not allied to the curvature of space-time and, as a result, it can be described in the framework of the special relativity.https://www.maplesoft.com/applications/view.aspx?SID=1469&ref=FeedMon, 16 May 2005 00:00:00 ZDr. Friedrich FUTSCHIKDr. Friedrich FUTSCHIKAn Algorithm to Approximate Pi
https://www.maplesoft.com/applications/view.aspx?SID=1442&ref=Feed
This worksheet demonstrates the use of Maple to show how to approximate the ratio between the perimeter and the diameter of a circle. Since the 18th century this ratio has been known as Pi, and since 1882 it had been known to be a transcendent number. This is an irrational number, which satisfies no algebraic equation but can be calculated, by means of infinite series, to any desired number of decimal places. Using computers, Pi has been calculated to over 200,000,000,000 digits.
In this worksheet, the author uses Maple to implement Archimedesâ€™s method for calculating Pi.<img src="https://www.maplesoft.com/view.aspx?si=1442/approxpi_5.gif" alt="An Algorithm to Approximate Pi" style="max-width: 25%;" align="left"/>This worksheet demonstrates the use of Maple to show how to approximate the ratio between the perimeter and the diameter of a circle. Since the 18th century this ratio has been known as Pi, and since 1882 it had been known to be a transcendent number. This is an irrational number, which satisfies no algebraic equation but can be calculated, by means of infinite series, to any desired number of decimal places. Using computers, Pi has been calculated to over 200,000,000,000 digits.
In this worksheet, the author uses Maple to implement Archimedesâ€™s method for calculating Pi.https://www.maplesoft.com/applications/view.aspx?SID=1442&ref=FeedThu, 03 Mar 2005 05:00:00 ZDr. Friedrich FUTSCHIKDr. Friedrich FUTSCHIK