Change In Angular Momentum Research Articles

Advantages of application of variational integrators on Lie groups in problems of modeling the dynamics of mechanical systems

Purpose of the research is to consider advantages of application of variational integrators on Lie groups in problems of physically correct modeling of dynamics of mechanical systems and to compare them with classical nonvariational integrators.Methods. To demonstrate the possibilities of variational integrators on Lie groups, a mathematical model of the dynamics of a physical pendulum was developed. Methods of variational calculus and methods of Lie group theory were used to construct a mathematical model of the dynamics of a physical pendulum. The Runge-Kutta method of the 4th order was used for comparative analysis of variational and nonvariational integrators. Modeling was carried out in MATLAB software.Results. In this research, a variational integrator algorithm on Lie groups was developed to model the dynamics of a physical pendulum. To compare the variational integrators and the 4th order Runge-Kutta method, plots were constructed to show how the angular velocity along the axes, orthogonal error, total energy, and angular momentum change over time. The graphs demonstrate that although the angular velocity is the same for both methods, the Runge-Kutta method does not preserve the geometric structure of the continuous system and does not preserve the basic constant quantities of the modeled system, namely mechanical energy and momentum.Conclusion. Numerical modeling has shown that the preservation of symplectic properties of systems and the structure of Lie groups allows to perform physically correct computer modeling of the dynamics of mechanical systems. Variational integrators on Lie groups have significant computational advantages over classical integration methods, which do not preserve the geometric structure of the continuous system and the basic constant quantities of the system, and other variational integrators, which preserve either none or one of these properties.

Balance training in older adults enhances feedback control after perturbations.

As we age, avoiding falls becomes increasingly challenging. While balance training can mitigate such challenges, the specific mechanisms through which balance control improves remains unclear. We investigated the impact of balance training in older adults on feedback control after perturbations, focusing on kinematic balance recovery strategies and muscle synergy activation. Twenty older adults aged over 65 underwent short-term (one session) and long-term (3-weeks, 10 sessions) balance training, and their recovery from unpredictable mediolateral perturbations was assessed. Perturbations consisted of 8° rotations of a robot-controlled platform on which participants were balancing on one leg. We measured full-body 3D kinematics and activation of 15 leg and trunk muscles, from which linear and rotational kinematic balance recovery responses and muscle synergies were obtained. Our findings revealed improved balance performance after long-term training, characterized by reduced centre of mass acceleration and (rate of change of) angular momentum. Particularly during the later stage of balance recovery the use of angular momentum to correct centre of mass displacement was reduced after training, decreasing the overshoot in body orientation. Instead, more ankle torque was used to correct centre of mass displacement, but only for perturbations in medial direction. These situation and strategy specific changes indicate adaptations in feedback control. Activation of muscle synergies during balance recovery was also affected by training, specifically the synergies responsible for leg stiffness and ankle torques. Training effects on angular momentum and the leg stiffness synergy were already evident after short-term training. We conclude that balance training in older adults refines feedback control through the tuning of control strategies, ultimately enhancing the ability to recover balance.

Understanding the puzzle of angular momentum conservation in beta decay and related processes

We ask the question of how angular momentum is conserved in electroweak interaction processes. To introduce the problem with a minimum of mathematics, we first raise the same issue in elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon, and note its presence in scattering of a fully relativistic spin-1/2 particle by a central potential. We then consider inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus. While both the incident neutrino and final electron spins are antiparallel to their momenta, the final spin is in a different direction than that of the neutrino-an apparent change of angular momentum. However, prior to measurement of the final particle, in all these cases angular momentum is indeed conserved. The apparent nonconservation of angular momentum arises in the quantum measurement process in which the measuring apparatus does not have an initially well-defined angular momentum, but is localized in the outside world. We generalize the discussion to massive neutrinos and electrons, and examine nuclear beta decay and electron-positron annihilation processes through the same lens, enabling physically transparent derivations of angular and helicity distributions in these reactions.

Design of optimum spacecraft reorientation control with a combined criteria of quality based on the quaternions

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs including the contribution of controlling torques and integral of rotary energy (in a known proportion) and reorientation time; presence of duration factor bounds time of rotation finish. To construct an optimal control of angular momentum changing, quaternionic method and the maximum principle were applied. Differential equation that relates spacecraft angular momentum and quaternion of spacecraft orientation is a base to obtain analytic solution to a problem. We reveal the properties of optimum control program analytically, and study key features of optimum motion in details. Also, we write the formalized equations, mathematical formulas to design optimal law for change of spacecraft’s angular momentum. Analytic relations and equations are given for finding the optimal solution. Control law (in as explicit dependence between phase variables and con-trolling variables has been formulated. Main relations determining optimum values of parameters for rotation control algorithm were given. The closed-form law for rotation was obtained for dynamically symmetric solids. Numerical example as well as results of mathematical modeling of spacecraft motion that formed using optimum control are presented. This data as addition to the made theoretic descriptions shows reorientation process (in virtual form) and demonstrates practical feasibility of the developed control method. A designed algorithm for optimal control of rotation improves an efficiency of attitude system, and originates more economical performing of space vehicle during its flight along orbit.

Design of optimum spacecraft reorientation control with a combined criteria of quality based on the quaternions

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs including the contribution of controlling torques and integral of rotary energy (in a known proportion) and reorientation time; presence of duration factor bounds time of rotation finish. To construct an optimal control of angular momentum changing, quaternionic method and the maximum principle were applied. Differential equation that relates spacecraft angular momentum and quaternion of spacecraft orientation is a base to obtain analytic solution to a problem. We reveal the properties of optimum control program analytically, and study key features of optimum motion in details. Also, we write the formalized equations, mathematical formulas to design optimal law for change of spacecraft’s angular momentum. Analytic relations and equations are given for finding the optimal solution. Control law (in as explicit dependence between phase variables and con-trolling variables has been formulated. Main relations determining optimum values of parameters for rotation control algorithm were given. The closed-form law for rotation was obtained for dynamically symmetric solids. Numerical example as well as results of mathematical modeling of spacecraft motion that formed using optimum control are presented. This data as addition to the made theoretic descriptions shows reorientation process (in virtual form) and demonstrates practical feasibility of the developed control method. A designed algorithm for optimal control of rotation improves an efficiency of attitude system, and originates more economical performing of space vehicle during its flight along orbit.

Self-similar Buildup and Inside-out Growth: Tracing the Evolution of Intermediate-to-high-mass Star-forming Galaxies since z = 2

We aim to discern scenarios of structural evolution of intermediate-to-high-mass star-forming galaxies (SFGs) since cosmic noon by comparing their stellar mass profiles with present-day stellar masses of log(M*,0/M⊙)=10.3−11 . We addressed discrepancies in the size evolution rates of SFGs, which may be caused by variations in sample selection and methods for size measurements. To check these factors, we traced the evolution of individual galaxies by identifying their progenitors using stellar mass growth histories (SMGHs), integrating along the star-forming main sequence and from the IllustrisTNG simulations. Comparison between the structural parameters estimated from the mass- and light-based profiles shows that mass-weighted size evolves at a slower pace compared to light-based ones, highlighting the need to consider the mass-to-light ratio (M/L) gradients. Additionally, we observed mass-dependent growth in stellar mass profiles: massive galaxies ( log(M*,0/M⊙)≳10.8 ) formed central regions at z ≳ 1.5 and grew faster in outer regions, suggesting inside-out growth, while intermediate-mass and less massive SFGs followed a relatively self-similar mass buildup since z ∼ 2. Moreover, slopes of observed size evolution conflict with the predictions of TNG50 for samples selected using the same SMGHs across our redshift range. To explore the origin of this deviation, we examined changes in angular momentum (AM) retention fraction using the half-mass size evolution and employing a simple disk formation model. Assuming similar dark matter halo parameters, our calculations indicate that the AM inferred from observations halved in the past 10 Gyr while it remained relatively constant in TNG50. This higher AM in simulations may be due to the accretion of high-AM gases into disks.

Horizon fluxes of binary black holes in eccentric orbits

We compute the rate of change of mass and angular momentum of a black hole, namely tidal heating, in an eccentric orbit. The change is caused due to the tidal field of the orbiting companion. We compute the result for both the spinning and non-spinning black holes in the leading order of the mean motion, namely ξ. We demonstrate that the rates get enhanced significantly for nonzero eccentricity. Since eccentricity in a binary evolves with time we also express the results in terms of an initial eccentricity and azimuthal frequency ξϕ. In the process, we developed a prescription that can be used to compute all physical quantities in a series expansion of initial eccentricity, e0. These results are computed taking account of the spin of the binary components. The prescription can be used to compute very high-order corrections of initial eccentricity. We use it to find the contribution to eccentricity up to O(e05) in the spinning binary. Using the computed expression of eccentricity, we derived the rate of change of mass and angular momentum of a black hole, both rotating and non-rotating, in terms of initial eccentricity and azimuthal frequency up to O(e06). With the computed fluxes we also compute for the first time the leading order dephasing in both cases analytically up to O(e06) and study its impact. We argue that for high signal-to-noise ratio sources, these contributions require inclusion in the waveform modeling.

Exploring waveforms with non-GR deviations for extreme mass-ratio inspirals

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity.

Exploring the control of whole-body angular momentum in young and elderly based on the virtual pivot point concept.

While walking, ground reaction forces point from the centre of pressure to the neighbourhood of a focal point, namely the virtual pivot point (VPP), that adjusts angular momentum around the centre of mass (CoM). This study explores how age and speed affect the VPP quality and position during walking. Analysing an experimental dataset reveals high quality of the VPP in the sagittal plane for both young and elderly groups, regardless of speed. However, in the frontal plane, the VPP quality decreases with increasing speed, with elderly participants exhibiting significantly lower quality. Although not a direct measure of balance, VPP quality reflects changes in whole-body angular momentum owing to ageing and speed. Additionally, a template model is used to reproduce the VPP quality and position trends observed in the experiment. Simulation results highlight the sensitivity of VPP quality to leg force feedback and show that changing VPP height has minimal effect on gait speed. Furthermore, energy redistribution occurs through increased hip extension and leg damping, associated with a greater horizontal VPP distance from the CoM, observed in elderly walking. This study shows promise for analysing gait based on VPP, potentially aiding clinical interventions and supporting locomotion in the elderly.

Healthy older adults generate transverse-plane momenta required for 90° turns while walking during the same phases of gait as used in straight-line gait

BackgroundGeneration and regulation (control) of linear and angular momentum is a challenge during turning while walking which may be exacerbated by age-related changes. In healthy older adults, little is known about how momentum is controlled during turns, especially within each phase of gait. Each phase of gait affords unique mechanical contexts to control momenta and regulate balance. In healthy young adults, we found that the transverse-plane linear and angular momenta generation strategies observed within specific phases of gait during straight-line gait were also used during turns. Therefore, in this study, we investigated whether healthy older adults shared similar momentum control strategies specific to each gait phase during straight-line gait and turns.MethodsNine healthy older adults completed straight-line gait and 90° leftward walking turns. We compared the change in transverse-plane whole-body linear and angular momentum across gait phases (left and right single and double support). We also compared the average leftward force and transverse-plane moment across gait phases.ResultsWe found that leftward linear momentum was generated most during right single support in straight-line gait and leftward turns. However, in contrast to straight-line gait, during leftward turns, average leftward force was applied across gait phases, with left single support generating significantly less leftward average force than other gait phases. Leftward angular momentum generation and average moment were greatest during left double support in both tasks. We observed some within-participant results that diverged from the group statistical findings, illustrating that although they are common, these momenta control strategies are not necessary.ConclusionsOlder adults generated transverse-plane linear and angular momentum during consistent phases of gait during straight-line gait and 90° turns, potentially indicating a shared control strategy. Understanding momentum control within each phase of gait can help design more specific targets in gait and balance training interventions.

Hawking Temperature Modification and the Physical Dynamics of Black Holes: A Study of the Influence of Internal and Cosmological Variables

<p>The main objective of the study is to develop a model that modifies the traditional Hawking temperature by considering the influence of internal variables such as radius, mass, electric charge, angular momentum, and cosmological constant. The research method involves mathematical analysis and computational modeling based on the modified Hawking temperature equation. The results show that the modified Hawking temperature produces non-linear corrections that show the interaction between black holes and the quantum structure of spacetime. graphical representations visualize the variation of Hawking temperature with changes in area, electric charge, angular momentum, and cosmological parameters. The implications of the research extend to the understanding of the thermal properties of black holes in the context of gravitational and quantum theories. The research identifies gaps in the knowledge of the effects of cosmological parameters on black hole thermodynamics and introduces Hawking temperature modifications that have not been mapped in detail before. The study concludes that the Hawking temperature modification provides a strong foundation for further research in black hole physics, particularly in the effect of physical and cosmological parameters on the thermal properties of black holes.</p>

Oblique impingement of binary droplets at the nanoscale on superhydrophobic surfaces: A molecular dynamics study.

The impacting phenomenon of nanodroplets has received much attention due to their importance in various industrial applications. The oblique impingement of single droplets is well understood; however, the effect of oblique angle on impacting the dynamics of multiple droplets at the nanoscale is very limited. To address this gap, we perform molecular dynamics (MD) simulations to study the impacting dynamics of binary nanodroplets with various oblique angles (αob) and Weber numbers (We). Using MD simulations, we directly capture the detailed morphological evolution of the impacting binary droplets with various given conditions. Compared to the oblique impingement of a single droplet, the evolution of impacting binary droplets involves two novel dynamic characteristics: the asymmetric dynamics with droplet preferential spreading in the y direction and the rotating of the coalescing droplet. The mechanisms underlying are well studied. The asymmetric dynamics is a result of the velocity gradient of the outer edge of the spreading droplet, and the rotating effect is due to the change in angular momentum induced by surface force. The analysis and study of these phenomena have never been mentioned in previous studies of single droplet. Finally, we investigate the effect of αob and We on normalized moving distance (L/Dsin) and contact time (tc). This work paves the way for offering a comprehensive understanding of the oblique impingement of binary nanodroplets.

Skillful prediction of length of day one year ahead in multiple decadal prediction systems

Despite a small amplitude, Length of Day (LOD) change, which varies from one year to another due to changes in Atmospheric Angular Momentum (AAM), determines the accuracy of Global Positioning System (GPS) time calculation. In this study, we examine the prediction skill of LOD and AAM in nine decadal prediction systems archived for the Decadal Climate Prediction Project. A persistence and rebound in LOD prediction skill at one year or longer lead time is found in most models. A poleward propagation of AAM anomaly via wave-mean flow interaction is also qualitatively well reproduced. This long-lead prediction of LOD and AAM is attributed to reliable predictions of the El Niño–Southern Oscillation (ENSO) and the Quasi-Biennial Oscillation (QBO), the former being more systematically related than the latter. This result indicates that the improved ENSO prediction and atmospheric wave-mean flow interaction may lead to better prediction of LOD, AAM and related extratropical climate in the decadal prediction systems.

Emission of twisted photons by a Dirac electron in a strong magnetic field

We study the spontaneous emission of a photon during the transitions between relativistic Landau states of an electron in a constant magnetic field that can reach the Schwinger value of Hc=4.4×109 T. In contrast to the conventional method, in which detection of both the final electron and the photon are implied in a certain basis, here we derive the photon state as it evolves from the process itself. It is shown that the emitted photon state represents a twisted Bessel beam propagating along the field axis with a total angular momentum (TAM) projection onto this axis ℓ−ℓ′, where ℓ and ℓ′ are the TAM of the initial electron and of the final one, respectively. Thus, the majority of the emitted photons turn out to be twisted, with ℓ−ℓ′≳1, even when the magnetic field reaches the critical value of H∼Hc. The transitions without a change of the electron angular momentum, ℓ′=ℓ, are possible, yet much less probable. We also compare our findings with those for a spinless charged particle and demonstrate their good agreement for the transitions without change of the electron spin projection even in the critical fields, while the spin-flip transitions are generally suppressed. In addition, we argue that whereas the ambiguous choice of an electron spin operator affects the differential probability of emission, this problem can partially be circumvented for the photon evolved state because it is the electron TAM rather than the spin alone that defines the TAM of the emitted twisted photon. Published by the American Physical Society 2024

Synthesis of Optimal Control of Spacecraft Angular Momentum for Spatial Turn Taking into Account Energy Costs Using Quaternions

Background: In this paper, we propose solving the specific original problem of control synthesis of spacecraft attitude. Optimization of the control program is made with the use of a new criterion of quality that combines energy costs and duration of reorientation under restrictions on control (the presence of a time factor limits the duration of slew maneuver). Methods: The construction of optimal control for angular momentum change is based on the quaternion method and L.S. Pontryagin maximum principle. An analytical solution to the problem was obtained on the base of a differential equation relating the orientation quaternion and angular momentum of a spacecraft. Results: Key properties of the optimal solution are formulated in analytical form; the features of optimal motion are studied in detail. The control law is formulated in the form of explicit dependence between control and phase variables. In a case when the controlling torque is limited by the given restriction (at the beginning and end of a turn), analytical formulas have been written for the duration of braking and acceleration. Main relations which determine optimal values of parameters of the algorithm for control of angular momentum are given. Examples and results of mathematical modeling of spacecraft motion formed by optimal control were given. This data in addition to the theoretical descriptions illustrates the process of reorientation in evident form and demonstrates the practical feasibility of a designed method for control of angular momentum during spatial turn. Conclusion: The designed optimal algorithm of control of spacecraft motion improves the efficiency of spacecraft attitude system, and originates more economical performance of spacecraft during flight on orbit.

Triplet properties and intersystem crossing mechanism of PtAg28 nanocluster sensitizers achieving low threshold and efficient photon upconversion.

Ligand-protected metal nanoclusters have emerged as a promising platform for providing sensitizers for triplet-triplet annihilation upconversion (TTA-UC). Herein, we report [PtAg28(BDT)12]4- (PtAg28; BDT = 1,3-benzenedithiolate) as a sensitizer enabling TTA-UC at low excitation intensities. PtAg28 exhibits a long-lived triplet state (approximately 7 μs) generated with a 100% intersystem crossing (ISC) quantum yield. The mechanism driving this efficient ISC was unveiled with the aid of theoretical calculations. Specifically, the S1-T1 ISC reveals a small spin-orbit coupling (SOC) matrix element, attributed to their similar electron configuration. In contrast, the T2 state, which is energetically close to S1, features a hole distribution derived from the Py superatomic orbital of the icosahedral Pt@Ag12 core. This distribution enables direct SOC based on the orbital angular momentum change from the S1 state with a Pz-derived hole distribution. Consequently, the efficient ISC was rationalized by the S1 → T2 → T1 pathway. The T1 state possesses a metal core-to-surface metal charge transfer character, facilitating triplet energy transfer and conferring superior sensitization ability. Leveraging these characteristics, the combination of PtAg28 sensitizer with a 9,10-diphenylanthracene annihilator/emitter attained an extremely low UC threshold of 0.81 mW cm-2 at 532 nm excitation, along with efficient green-to-blue TTA-UC with an internal quantum yield (ΦUCg) of 12.2% (50% maximum). This results in a pseudo-first-order TTA process with strong UC emission under 1-sun conditions.

In-plane tidal disruption of stars in discs of active galactic nuclei

ABSTRACT Stars embedded in active galactic nucleus (AGN) discs or captured by them may scatter onto the supermassive black hole (SMBH), leading to a tidal disruption event (TDE). Using the moving-mesh hydrodynamics simulations with arepo, we investigate the dependence of debris properties in in-plane TDEs in AGN discs on the disc density and the orientation of stellar orbits relative to the disc gas (pro- and retro-grade). Key findings are: (1) Debris experiences continuous perturbations from the disc gas, which can result in significant and continuous changes in debris energy and angular momentum compared to ‘naked’ TDEs. (2) Above a critical density of a disc around an SMBH with mass M• [ρcrit ∼ 10−8 g cm−3 (M•/106 M⊙)−2.5] for retrograde stars, both bound and unbound debris is fully mixed into the disc. The density threshold for no bound debris return, inhibiting the accretion component of TDEs, is $\rho _{\rm crit,bound} \sim 10^{-9}{\rm g~cm^{-3}}(M_{\bullet }/10^{6}\, {\rm M}_{\odot })^{-2.5}$. (3) Observationally, AGN-TDEs transition from resembling naked TDEs in the limit of ρdisc ≲ 10−2ρcrit,bound to fully muffled TDEs with associated inner disc state changes at ρdisc ≳ ρcrit,bound, with a superposition of AGN + TDE in between. Stellar or remnant passages themselves can significantly perturb the inner disc. This can lead to an immediate X-ray signature and optically detectable inner disc state changes, potentially contributing to the changing-look AGN phenomenon. (4) Debris mixing can enrich the average disc metallicity over time if the star’s metallicity exceeds that of the disc gas. We point out that signatures of AGN-TDEs may be found in large AGN surveys.

Modulation of Mars’ diurnal polar motion by atmospheric dust cycles

The atmospheric dust cycle plays a crucial role in impacting the atmosphere of Mars, and may also introduce changes in angular momentum that can influence the planet's polar motion. However, the potential connections between polar motion and atmospheric dust cycles have not yet been explored. In this study, we computed atmosphere-excited polar motion and the atmospheric dust cycle index (ADCI) separately from the Mars Climate Database and observed dust optical depth for Martian Years 24–33. We found a strong correlation between diurnal polar motion amplitude change and ADCI, with significance levels above 99%. Our results suggest that atmospheric dust cycles significantly modulate diurnal polar motion. Wavelet transform analyses further revealed other factors, such as water ice clouds, may be responsible for higher frequency modulations of polar motion apart from the dust-related signals. Interdisciplinary studies involving Mars' atmospheric activities and rotational variations can significantly advance our understanding of planetary atmospheric science and global rotational dynamics.

Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency.

For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.

A Dynamicly Consistent Model of Normal Reactions at Points of a Mobile Platform Contact with a Surface Taking Account of the Design of Mecanum Wheels and Multicomponent Friction

The article investigates the influence of the dependence of normal reactions on motion parameters on the dynamics of a mobile platform by taking into account the design of mecanum wheels and multicomponent friction. To describe the dependence of normal reactions on motion parameters, the theorems on the change in momentum and angular momentum written for the mecanum platform are used. The influence of normal reactions on the dynamics of the mecanum platform is estimated from the results of numerical simulation. The mecanum platform dynamics model takes into account the design of the mecanum wheels and multicomponent friction. The multicomponent friction model proposed by V.F. Zhuravlev that takes into account sliding and spinning is considered. Estimates of the maximum deviations of the normal reactions of the supports, due to the dynamics of the mecanum platform, from the values of the normal reactions calculated for the mobile platform at rest (equal to 16.7% for KUKA youBot robot) are given. Inequalities that limit the maximum values of the control moments, under which the contacting rollers of the mecanum wheels do not come off from the supporting surface are obtained. Based on the simulation results, it is shown that the normal responses are changed by 5–6% of the normal response value calculated in the case of the mecanum platform at rest, which corresponds to the obtained estimates. These changes in normal reactions can lead to a decrease in the accuracy of the movement of the mecanum platform obtained with program control.