In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles where is the Cartesian coordinate of the position vector of the particle. The origin of the coordinate system has been chosen such that i.e. in the system of the center of mass . Where Another definition, which is mathematically identical but gives an alternative calculation method, is: Therefore, the x-y component of the gyration tensor for particles in Cartesian coordinates would be: In the continuum limit, where represents the number density of particles at position . Although they have different units, the gyration tensor is related to the moment of inertia tensor. The key difference is that the particle positions are weighted by mass in the inertia tensor, whereas the gyration tensor depends only on the particle positions; mass plays no role in defining the gyration tensor. (Wikipedia).
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
From playlist What is a Tensor?
Tensors Explained Intuitively: Covariant, Contravariant, Rank
Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
What is a Tensor? Lesson 17: The covariant derivative (elementary pedagogy)
What is a Tensor? Lesson 17: The covariant derivative (elementary pedagogy)
From playlist What is a Tensor?
Calculus 3: Tensors (1 of 28) What is a Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t
From playlist CALCULUS 3 CH 10 TENSORS
What is a Tensor? Lesson 29: Transformations of tensors and p-forms (part review)
What is a Tensor? Lesson 29: Tensor and N-form Transformations This long lesson begins with a review of tensor product spaces and the relationship between coordinate transformations on spacetime and basis transformations of tensor fields. Then we do a full example to introduce the idea th
From playlist What is a Tensor?
A review of the notes common to all formations of a G chord.
From playlist Music Lessons
Lek-Heng Lim: "What is a tensor? (Part 1/2)"
Watch part 2/2 here: https://youtu.be/Lkpmd5-mpHY Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "What is a tensor? (Part 1/2)" Lek-Heng Lim - University of Chicago, Statistics Abstract: We discuss the three best-known definitions of a tensor:
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Mechanical Engineering: Ch 12: Moment of Inertia (33 of 97) What is the Radius of Gyration?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain conceptually what is the radius of gyration (of an area). Next video in this series can be seen at: https://youtu.be/z9za6ztZ-ME
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (34 of 97) Radius of Gyration: Calculated
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the radius of gyration of a square. Next video in this series can be seen at: https://youtu.be/0nK-YZc_Cw0
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (35 of 97) Radius of Gyration (Area): Ex 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the radius of gyration of an area bounded by y=kx^2 (relative to the x-axis). Next video in this series can be seen at: https://youtu.be/S4uoDoNN0ro
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
James D. Callen: Fluid and transport modeling of plasmas 2: kinetic and fluid solutions of PKE
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Physics
Aurora Clark (5/26/21): Multiscale Many-body Correlations and Structure in Chemistry Data
Full Title: Multiscale Many-body Correlations and Structure in Chemistry Data – Integrating Graphs, Topology and Geometry to Provide Fundamental Insight Abstract: Although Chemistry is inherently mathematical and foundational theories rely upon beautiful and complex applications of differ
From playlist AATRN 2021
Mechanical Engineering: Ch 12: Moment of Inertia (36 of 97) Radius of Gyration (Area): Ex 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the radius of gyration of an area bounded by y=kx^2 (relative to the y-axis). Next video in this series can be seen at: https://youtu.be/oXg5yv8_Sg4
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (43 of 97) = 2nd Moment of Area: Triangle 3/3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the moment of inertia (and second moment of area), I(y)=?, of a triangle: part 3/3. Next video in this series can be seen at: https://youtu.be/jPAF8pudeDk
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Topics in Protein folding by D. Thirumalai
Conference and School on Nucleation Aggregation and Growth URL: https://www.icts.res.in/program/NAG2010 DATES: Monday 26 July, 2010 - Friday 06 Aug, 2010 VENUE : Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru DESCRIPTION: Venue: Jawaharlal Nehru Centre for Advance
From playlist Conference and School on Nucleation Aggregation and Growth
Understanding the Area Moment of Inertia
The area moment of inertia (also called the second moment of area) defines the resistance of a cross-section to bending, due to the shape of the cross-section. It is a key parameter for the analysis of beams and columns. In this video I take a detailed look at the area moment of inertia,
From playlist Mechanics of Materials / Strength of Materials
Protein Collapse and Folding by Govardhan Reddy
Indian Statistical Physics Community Meeting 2016 URL: https://www.icts.res.in/discussion_meeting/details/31/ DATES Friday 12 Feb, 2016 - Sunday 14 Feb, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community wh
From playlist Indian Statistical Physics Community Meeting 2016
Calculus 3: Tensors (13 of 45) What is the Inertia Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the inertia tensor relating the physical inertia activity and the tensor component notation. Next video in the series can be seen at: https://youtu.be/-chgCHuEI4Y
From playlist CALCULUS 3 CH 10 TENSORS