Related papers: Quaternions in collective dynamics
In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
The individual-based models constitute a set of widely implemented tools to analyze the incidence of individuals heterogeneities in the spread of an infectious disease. In this work we focus our attention on human contacts heterogeneities…
Motivated by the need to predict dangerous scenarios, this article introduces a non-linear dynamic model for motorcycles consisting of four rigid bodies. Using Jourdain's principle, the model incorporates both longitudinal and lateral…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this…
This paper presents a novel end-to-end deep learning framework for real-time inertial attitude estimation using 6DoF IMU measurements. Inertial Measurement Units are widely used in various applications, including engineering and medical…
Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are…
Social identities play an important role in the dynamics of human societies, and it can be argued that some sense of identification with a larger cause or idea plays a critical role in making humans act responsibly. Often social activists…
In active matter and living matter, such as clusters of migrating cells, collective dynamics emerges from the underlying interactions. A common assumption of theoretical descriptions of collective cell migration is that these interactions…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
Human interactions are influenced by emotions, temperament, and affection, often conflicting with individuals' underlying preferences. Without explicit knowledge of those preferences, judging whether behaviour is appropriate becomes…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
We discuss the application of a theory of large-amplitude collective motion to a simple model mimicking the pairing-plus-quadrupole model of nuclear physics.
We study a system of self-propelled particles which interact with their neighbors via alignment and repulsion. The particle velocities result from self-propulsion and repulsion by close neighbors. The direction of self-propulsion is…
This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid…
A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. Evolution equations are shown to depend on higher-order gradients of the Hamiltonian, which are incorporated via their equations of…
The equations of the Newtonian $n$-body problem have a matrix form, where an $n\times n$ matrix depending on the masses and on the mutual distances appears as a factor. The $n$ eigenvalues of this matrix are real and nonnegative. In a…
Sensor network attitude problem consists in retrieving the attitude of each sensor of a network knowing some relative orientations between pairs of sensors. The attitude of a sensor is its orientation in an absolute axis system. We present…