Rotation Sequence Research Articles

Microstructure, crystallographic texture and strain hardening behavior in hot tensile tests of UNS S32304 Lean Duplex stainless steel

Duplex stainless steels can be used for applications in the nuclear industry endorsing its choice as an external shield for Type B packages. The microstructure, crystallographic texture, and the strain hardening behavior of UNS S32304 duplex stainless steel was investigated in hot tensile tests by Electron Backscattering Diffraction technique. Interrupted hot tensile tests with strain rates ε˙ = 10−2 s−1 and ε˙ = 10−1 s−1 were carried out at 700 °C using a Thermomechanical Physical simulator. The α parameter of gamma distribution was associated for the first time with strain in ferrite and austenite phases through the Grain Orientation Spread parameter (GOS). The ferrite phase did not show the dynamic equilibrium between the stored energy and recovery rates. The average GOS in the ferrite phase was larger for ε˙ = 10−1 s−1 due to a smaller time available for dislocation annihilation and rearrangement in dynamic recovery. The grain rotation sequence <100> → <100> - <101> → <101> was found in ferrite phase. In the austenite phase, the dynamic recrystallization was not observed and the <111> and <100> fiber textures parallel to the tensile direction were strengthened. The austenite → ferrite phase transformation occurred during the hot tensile tests and showed the Kurdjumov-Sachs orientation relationship. The modified Crussard-Jaoul analysis showed six-strain hardening stages which were associated with the average GOS and austenite → ferrite phase transformation.

The improvement of the winter wheat cultivation technology in arid conditions of the Povolzhie

Winter wheat is currently the main grain field crop in the European part of Russia. However, to increase the cultivation efficiency, it is necessary to improve cultivation technology. The purpose of the work is to identify new promising varieties and improve the winter bread wheat cultivation technology for the arid conditions of the Povolzhie. In 2015–2019 there was conducted an agroecological testing for 17 winter wheat varieties, which were most widespread and had the prospects for their introduction in the Povolzhie. During 2011–2018 there were studied five cultivation technologies (options) of the winter wheat variety ‘Svetoch’ in the six crop rotation sequences. The study has established that when cultivating winter wheat in the blackearth (chernozem) steppe of the Povolzhie, the varieties ‘Marafon’, ‘Novoershovskaya’, ‘Zhemchuzhina Povolzhiya’, ‘Severodonetskaya yubileynaya’ and ‘Svetoch’ were the most promising varieties. Under favorable moisture conditions, it was most profitable to cultivated the varieties ‘Rostovchanka 7’, ‘Izyuminka’, ‘Marafon’, ‘Bazis’, ‘Severodonetskaya yubileynaya’, ‘Skipetr’. When cultivating winter wheat in ‘black’ fallow, it is more rational to use early fallow, which begins to be cultivated in the spring when the soil is physically matured. The early spring additional fertilizing with ammonium nitrate increases winter wheat productivity on 0.28 t/ha (9.3%). In order to obtain the maximum net income (11324.8 rubles/ha) and profitability (115.0%), it is most expedient to use the biological product ‘Bionex Kemi’ (3 l/ha) on commercial wheat crops.

Soil health conditions under cotton production in North Carolina

AbstractSoil organic carbon (SOC) and N fractions are considered important indicators of soil health due to their multifunctional roles in storing and supplying nutrients, enhancing soil physical properties, and feeding soil biological activity and plant nutrition. Soil health condition from 120 fields under cotton (Gossypium hirsutum L.) cultivation in North Carolina was assessed from soil analyses associated with a survey of historical management. Surface residue was collected, and soil was sampled at 0‐to‐10‐cm, 10‐to‐30‐cm, and 30‐to‐60‐cm depths. Soil properties varied by physiographic region of Piedmont, Coastal Plain, and Flatwoods. Conservation tillage was the dominant form of cotton cultivation, but many farms used inversion tillage for other crops in the rotation sequence. Soil‐test biological activity averaged 138 and 92 mg kg−1 3 d−1 under continuous conservation tillage and frequent tillage, respectively, in the surface 10‐cm depth (p &lt; .001), and the tillage effect persisted into the 10‐to‐30‐cm depth (44 and 37 mg kg−1 3 d−1, p &lt; .05). Cover cropping and animal manure had fewer and smaller effects on soil properties. History of animal manure application elevated (p &lt; .05) soil‐test P (229 vs. 179 g m−3), Cu (4.3 vs. 1.6 g m−3), and Zn (10.0 vs. 4.0 g m−3). Intermittent tillage in the rotation sequence was the largest impediment to sustained SOC, total soil N accumulation, and soil microbial properties. This assessment illustrated positive soil health condition from farmer adoption of conservation tillage, but further improvements will be possible only with more continuous practice of conservation approaches.

Agricultural Crop Change in the Willamette Valley, Oregon, from 2004 to 2017

The Willamette Valley, bounded to the west by the Coast Range and to the east by the Cascade Mountains, is the largest river valley completely confined to Oregon. The fertile valley soils combined with a temperate, marine climate create ideal agronomic conditions for seed production. Historically, seed cropping systems in the Willamette Valley have focused on the production of grass and forage seeds. In addition to growing over two-thirds of the nation’s cool-season grass seed, cropping systems in the Willamette Valley include a diverse rotation of over 250 commodities for forage, seed, food, and cover cropping applications. Tracking the sequence of crop rotations that are grown in the Willamette Valley is paramount to answering a broad spectrum of agronomic, environmental, and economical questions. Landsat imagery covering approximately 25,303 km2 were used to identify agricultural crops in production from 2004 to 2017. The agricultural crops were distinguished by classifying images primarily acquired by three platforms: Landsat 5 (2003–2013), Landsat 7 (2003–2017), and Landsat 8 (2013–2017). Before conducting maximum likelihood remote sensing classification, the images acquired by the Landsat 7 were pre-processed to reduce the impact of the scan line corrector failure. The corrected images were subsequently used to classify 35 different land-use classes and 137 unique two-year-long sequences of 57 classes of non-urban and non-forested land-use categories from 2004 through 2014. Our final data product uses new and previously published results to classify the western Oregon landscape into 61 different land use classes, including four majority-rule-over-time super-classes and 57 regular classes of annually disturbed agricultural crops (19 classes), perennial crops (20 classes), forests (13 classes), and urban developments (5 classes). These publicly available data can be used to inform and support environmental and agricultural land-use studies.

Weed seedbank diversity and sustainability indicators for simple and more diverse cropping systems

AbstractStorkey and Neve (2018) hypothesised that weed seedbank diversity could be used as an indicator of agroecosystem sustainability, with cropping systems associated with higher weed seedbank diversity being more agronomically and environmentally sustainable than those with lower weed diversity. We evaluated their hypothesis using multiple years of empirical data collected from a long‐term field experiment in Iowa, USA, and life cycle assessment models parameterised with data from that experiment. We found that diversifying a 2‐year maize–soyabean rotation with two additional crop phases, oat and lucerne, to form a 4‐year rotation (a) increased Simpson's diversity index for weed species in the soil seedbank, while (b) increasing maize and soyabean productivity, (c) maintaining total crop energy production and profitability, and (d) reducing herbicide‐related aquatic toxicity, fossil energy consumption, greenhouse gas emissions, damage to human health due to fine particulate matter, and discharge of soil sediment, nitrogen, and phosphorus. Increased weed biomass production and greater weed species diversity that occurred within oat and lucerne phases of the 4‐year rotation sequence did not result in a loss of weed control within maize and soyabean phases of the rotation. We suggest that while there was no cause‐and‐effect relationship between greater weed seedbank diversity and improved agroecosystem sustainability in agronomic, economic and environmental dimensions, all of these responses were driven in a parallel manner by cropping system diversification. Consequently, weed seedbank diversity may indeed be a useful agroecosystem sustainability indicator. Further evaluation of this hypothesis in more systems is warranted.

Remastering the imperfect home-made CT projections data for further reconstruction

We developed and implemented a few strategies to recover the faulty, randomly shifted, off-axis rotation sequence of projections images for the home-made computed tomography. Features detection, homography and other image transformation and processing tools from the open-source free and non-free OpenCV libraries in C++ were used. The developed methods, routines and implemented strategies could be collected into the standalone library for any home-made CT software packages.

Control of following Force in Gimbal Suspension by Programmed Transfer of Vehicle in the Class of Spiral-Screw Trajectories

The programmed transfer of the transport vehicle in space is carried out in the class of helical trajectories, using forcing (throttling) and deviation of the following driving force in the gimbal. The paper introduces the mathematical models of the transport vehicle kinetics in space in the terrestrial reference system and in the basis of the natural trihedral of the trajectory, using the quaternion form. The kinematics of the transport vehicle in the fixed and mobile reference systems, as well as the orientation of the natural trihedral in the inertial space, are represented by the hodograph of the program helix trajectory in vector and quaternion forms. The components of the controlling driving force in the basis of the natural trihedral are determined by the kinetostatics equations of the programmed transfer of the transport vehicle along a helical trajectory in the required speed mode. The authors proposed a structural scheme of the gimbal suspension, providing the required driving force components. The authors considered two possible sequences of rotations of the moving gimbal rings and demonstrated their equivalence. Laconic formulas are established for the control angles of rotation of the moving gimbal rings.

Plant-soil feedback responses of four dryland crop species under greenhouse conditions.

Plant-soil feedbacks (PSFs) give a mechanistic understanding on how soil properties established by previous plant species go on to influence the performance of the same or different species in monoculture, intercropping or crop rotation systems. We hypothesized that different dryland crops such as Zea mays L., Helianthus annuus L., Phaseolus vulgaris L., and Glycine max L. (Merr.) will have soil legacies that are related to the crop type. We used a two-phase experiment to test plant performance in soils previously cultivated with the same or different plant species under greenhouse conditions. The positive plant growth for all species in their own soil microbiota suggests that mutualists had a greater impact on plant performance than pathogens. The consistent positive soil-feedback results of P. vulgaris were strongly associated with their own beneficial soil microbiota, meaning that the conditioning phase legacy of mutualists and decomposers were more significant than pathogens under monoculture. Despite successful nodulation in sterilized and inoculated soils, G. max unexpectedly showed neutral and insignificant positive plant feedbacks, respectively. Helianthus annuus was superior to other crop species in creating active carbon stocks and an enzymatically active soil for the next crop. Microbial biomass results suggest that raising fungal relative to bacterial biomass can be achieved by increasing the frequency of H. annuus in rotation sequences. However, more studies are necessary to evaluate whether these elevated ratios promote or depress plant performance under field conditions. This study showed that relative to other dryland crops, H. annuus seems to have the potential of increasing fungal to bacterial ratios, raising legacies in active carbon stocks and soil microbial activity that may be crucial to successional planting in dryland systems.

Agricultural landscape-scale C factor determination and erosion prediction for various crop rotations through a remote sensing and GIS approach

In arable land management, different crop rotation patterns and sequences, such as changing agricultural land use to erosion prone crops, or crops providing less ground cover, can greatly influence soil loss rate through their impact on soil cover status (C factor value). The influence of crop rotation on C value and on erosion rate is often determined on an experimental plot scale, so the results are often erroneous when extrapolated to large heterogeneous landscapes, where they fail to capture the spatiotemporal variability beyond the experimental sites. In the present study we have endeavored to investigate the impact of various crop rotation patterns on C value and on subsequent soil erosion rate, at a landscape level, by combining 28 time-series satellite images (from 2013 to 2016) along with annually updated land-use data, via the integrated administration and control system (IACS), from the Uckermark district of north eastern Germany. In total, 21 different crop sequences were investigated. Winter wheat (WW), winter rape (WR), and maize (Mz) were found to be the predominant arable crops grown in the study area. The highest average annual C values were estimated from crop sequences involving Mz and sugar beet (SB), both as pre-crops and succeeding crops. The highest value of 0.39 was computed from SB/Mz rotation. On the other hand, crop rotation involving WR gave significantly lower annual C values in all the years considered, with the lowest average annual C value of 0.07 calculated on WR parcels preceded by winter cereals. It was also apparent that crop rotation patterns influenced C value in a temporally variable manner. Among the self-sequencing patterns, WR/WR reduced the C value significantly compared with Mz/Mz and to a lesser extent compared with WW/WW. Continuous cultivation of Mz increased the potential soil loss rate by as much as 72 % compared to WR/WR and by 51 % compared to WW/WW. It was also possible to determine the spatial distribution of the impact of crop rotation on soil erosion risk within the study area. The results obtained agreed with the results of other international and regional studies. Overall, the output from this research could contribute towards further efficient investigation of the impact of agronomic practices on the environment in a large agricultural landscape, without the need to set up multi-location experimental plots.

Lightweight Image Encryption: A Chaotic ARX Block Cipher

Nowadays, lightweight cryptography attracts academicians, scientists and researchers to concentrate on its requisite with the increasing usage of low resource devices. In this paper, a new lightweight image encryption scheme is proposed using the Lorenz 3D super chaotic map. This encryption scheme is an addition–rotation–XOR block cipher designed for its supremacy, efficacy and speed execution. In this addition–rotation–XOR cipher, the equation for Lorenz 3D chaotic map is iteratively solved to generate double valued signals in a speedy manner using the Runge–Kutta and Euler methods. The addition, rotation and diffusion sequences are generated from the double valued signals, and the source pixels of the 8-bit plain test images are manipulated with the addition, rotation and diffusion of the bytes. Finally, the cipher images are constructed from the manipulated pixels and evaluated with various statistical as well as randomness tests. The results from various tests prove that the proposed chaotic addition–rotation–XOR block image cipher is efficient in terms of randomness and speed.

Tomato and Melon Meloidogyne Resistant Rootstocks Improve Crop Yield but Melon Fruit Quality Is Influenced by the Cropping Season.

Four rotation sequences consisting of ungrafted tomato cv. Durinta – melon cv. Paloma or tomato grafted onto the resistant rootstock ‘Aligator’ – melon grafted onto the resistant Cucumis metuliferus accession BGV11135, and in reverse order, were conducted from 2015 to 2017 in a plastic greenhouse infested or not with Meloidogyne incognita to determine the plant tolerance (T), the minimum relative crop yield (m) and fruit quality. The relationship between M. incognita densities in soil at transplanting (Pi) of each crop and the crop yield was assessed and T and m were estimated by the Seinhorst’s damage model. In addition, the volume and the number of nuclei of single giant cells and the number of giant cells, its volume and the number of nuclei per feeding site in susceptible tomato and melon were compared to those in the resistant tomato and C. metuliferus 15 days after nematode inoculation in pot test. The relationship between the Pi and the relative crop yield fitted the Seinhorst’s damage model in both ungrafted and grafted tomato and melon, but not for all years and cropping seasons. The estimated T for ungrafted and grafted tomato did not differ but m was lower in the former (34%) than the latter (67%). Sodium concentration in fruits from ungrafted but not from grafted tomato increased with nematode densities in spring 2015 and 2016. The estimated ungrafted melon T did not differ from the grafted melon cultivated in spring, but it did when it was cultivated in summer. The relative crop yield of ungrafted melon was lower (2%) than the grafted cultivated in spring (62%) and summer (20%). Sodium concentration in melon fruits from ungrafted plants increased with nematode densities. No variations in fruit quality from grafted melon cultivated in spring were found, although less dry matter and soluble solid content at highest nematode densities were registered when it was cultivated in summer. Lower number of giant cells per feeding site was observed in both susceptible tomato germplasms compared to the resistant ones but they were more voluminous and held higher number of nuclei per giant cell and per feeding site.

Agronomic and Economic Effects of Irrigation and Rotation in Peanut-based Cropping Systems

Although the Southeast U.S. receives an average annual precipitation of 1300 mm, crop yields are often limited by erratic seasonal rainfall distributions. Studies were conducted from 2001 through 2017 at the USDA/ARS Multi-crop Irrigation Research Farm in Shellman, GA (84.60 deg W, 30.7333 deg N) on a Greenville fine sandy loam (fine, kaolinitic, thermic Rhodic Kandiudults). The objective of this long-term study is to evaluate the effects of irrigation and crop rotation sequencing consisting of peanut, corn, and cotton on yield and net economic returns to both variable and total costs. Analysis included the entire study period and was also separated for years with below and above average rainfall. When averaged across all years, irrigation increased peanut, corn, and cotton yield and net returns compared with non-irrigation. Six different rotation sequences were addressed inclusive of continuous peanut, one year out of peanut with corn or cotton, and two years out of peanut with combinations of corn and cotton. In both irrigated and non-irrigated peanuts, the least and greatest yields were from continuous peanut and the two year out rotations, respectively. No peanut yield difference resulted with corn or cotton rotation partners for the rotation sequence. Length of rotation between peanut years did influence peanut yield and net returns. Profitability and optimal rotation sequence within any cropping system depended on irrigation, yield, crop price, and production costs for peanut, corn, and cotton.

The influence of soil tillage system on Salsola kali L. emergence during the fallow period within cereal fields

AbstractWith the move towards conservation agriculture, we have seen an increase in weeds such as Salsola kali L., well known as Russian thistle, which are wind spread over fallow land. The emergence of this weed species seemed erratic, perhaps connected to climate conditions and management techniques. In order to shed some light on this issue, we carried out a field experiment over 3 years to monitor Russian thistle density in fallow plots, comparing three tillage systems. This study provides an insight about the limitations of assuming no‐tillage techniques within a cropping system that include fallow in the rotation sequence. Our results show that no‐tillage systems are more vulnerable to S. kali. Low spring rain leads to high S. kali density, especially in no‐tillage plots. High spring rainfall reduced the emergence in all tillage systems because of soil water saturation. Minimum tillage technique served to maintain control over this species even in weather conditions that favoured its emergence in other systems. In order to reduce the need for herbicide in fallow lands under conservation systems, we recommend the implementation of minimum tillage to combat Russian thistle infestation.

The effect of crop rotation on performance and qualitative characteristics of sugar beet

Sugar beet and sugarcane are two major crops for sugar extraction throughout the world. However, the sugar beet importance is not just about sugar production but it also plays an important role in crop rotation and increased productivity in various industries as well as livestock feed. In this study the long-term (2009-16) field trial effect of alfalfa (4 years)-winter wheat (1 year)–fallow (1year)-sugar beet rotation on yield and quality parameters of sugar beet were evaluated for two consecutive rotations. The field trials were carried out at single location in Karaj, Iran, using randomized complete block design with four replications. Analysis of variance showed that the seasonal factors influenced different traits. In the first and second rotations, the root yield ranged from about 56.5 to 83.2 and 61.4 to 77.8 t ha-1, respectively with significant difference among cultivars in the first rotation. However, no significant difference was observed among both rotations in terms of root yield. Same results were obtained for sugar yield in both rotations which illustrates the stability of the above-mentioned traits. Except for sugar content, significant difference was observed among other traits in both rotations. We show for the first time the effect of completing two rotation sequences on sugar beet performance and quality for decision making into a continual expansion/development of crop cultivation.

MotioNet

We introduce MotioNet , a deep neural network that directly reconstructs the motion of a 3D human skeleton from a monocular video. While previous methods rely on either rigging or inverse kinematics (IK) to associate a consistent skeleton with temporally coherent joint rotations, our method is the first data-driven approach that directly outputs a kinematic skeleton, which is a complete, commonly used motion representation. At the crux of our approach lies a deep neural network with embedded kinematic priors, which decomposes sequences of 2D joint positions into two separate attributes: a single, symmetric skeleton encoded by bone lengths, and a sequence of 3D joint rotations associated with global root positions and foot contact labels. These attributes are fed into an integrated forward kinematics (FK) layer that outputs 3D positions, which are compared to a ground truth. In addition, an adversarial loss is applied to the velocities of the recovered rotations to ensure that they lie on the manifold of natural joint rotations. The key advantage of our approach is that it learns to infer natural joint rotations directly from the training data rather than assuming an underlying model, or inferring them from joint positions using a data-agnostic IK solver. We show that enforcing a single consistent skeleton along with temporally coherent joint rotations constrains the solution space, leading to a more robust handling of self-occlusions and depth ambiguities.

Expression of N-cycling genes of root microbiomes provides insights for sustaining oilseed crop production.

Agricultural production is dependent on inputs of nitrogen (N) whose cycle relies on soil and crop microbiomes. Crop diversification has increased productivity; however, its impact on the expression of microbial genes involved in N-cycling pathways remains unknown. Here, we assessed N-cycling gene expression patterns in the root and rhizosphere microbiomes of five oilseed crops as influenced by three 2-year crop rotations. The first phase consisted of fallow, lentil or wheat, and the second phase consisted of one of five oilseed crops. Expression of bacterial amoA, nirK and nirS genes showed that the microbiome of Ethiopian mustard had the lowest and that of camelina the highest potential for N loss. A preceding rotation phase of lentil significantly increased the expression of nifH gene by 23% compared with wheat and improved nxrA gene expression by 51% with chemical fallow in the following oilseed crops respectively. Lentil substantially increased biological N2 fixation and reduced denitrification in the following oilseed crops. Our results also revealed that most N-cycling gene transcripts are more abundant in the microbiomes associated with roots than with the rhizosphere. The outcome of our investigation brings a new level of understanding on how crop diversification and rotation sequences are related to N-cycling in annual cropping systems.

Alfalfa establishment by interseeding with silage corn projected to increase profitability of corn silage–alfalfa rotations

AbstractCorn (Zea mays L.) silage and alfalfa (Medicago sativa L.) rotations dominate dairy forage production in temperate regions, but low yields during establishment of spring seeded alfalfa limits productivity and profitability. Interseeding alfalfa with corn silage is a novel establishment method that could enhance environmental quality, alfalfa production, and farm income, but it also incurs additional costs. Forage yields derived from long‐term field studies in Wisconsin along with feed values and input costs from 2012 to 2017 were used to predict net returns of corn silage–alfalfa rotation sequences that utilized conventional spring seeding or interseeding for alfalfa establishment and cereal rye (Secale cereal L.) as a winter cover crop following corn silage. Interseeded rotations yielded annual net return of $303 to $367 ha−1, with a 3‐yr corn and 3‐yr alfalfa sequence identified as the most profitable. Conventional rotations provided lower annual net returns of $260 to $320 ha−1 and the most profitable was a 4‐yr corn and 4‐yr alfalfa sequence. Sensitivity analyses demonstrated that interseeded alfalfa had a robust economic benefit, with increased net returns obtained when the corn yield penalty was limited to less than 20% or the success rate of alfalfa establishment exceeded 49% of attempts for the most profitable interseeded rotation sequence. A plant protective chemical application to interseeded alfalfa provided a net economic benefit if it increased the success rate of alfalfa establishment by at least 16%. Interseeding alfalfa into corn silage is predicted to enhance profitability of corn–alfalfa based cropping systems.

LAN: A Materials Notation for Two-Dimensional Layered Assemblies.

Two-dimensional (2D) layered materials offer intriguing possibilities for novel physics and applications. Before any attempt at exploring the materials space in a systematic fashion, or combining insights from theory, computation, and experiment, a formal description of information about an assembly of arbitrary composition is required. Here, we introduce a domain-generic notation that is used to describe the space of 2D layered materials from monolayers to twisted assemblies of arbitrary composition, existent or not yet fabricated. The notation corresponds to a theoretical materials concept of stepwise assembly of layered structures using a sequence of rotation, vertical stacking, and other operations on individual 2D layers. Its scope is demonstrated with a number of example structures using common single-layer materials as building blocks. This work overall aims to contribute to the systematic codification, capture, and transfer of materials knowledge in the area of 2D layered materials.

A new aestivation strategy for land molluscs: hanging upside down like bats

Introduction: Many land molluscs survival strategies are still poorly understood or have not been even reported, especially in the Neotropics. Methods: I collected 25 adult Tikoconus (Tikoconus) costarricanus from Reserva Forestal Río Macho, Costa Rica. I kept the specimens for 8 days in terrariums to film their behavior. Objective: To analyse the behavior of T. costarricanus, with emphasis on its strategies to survive drought and probably also predation. Results: This snail has at least three unusual behaviors that probably help them reduce dehydration and may be escape from enemies and avoid diseases: hanging upside down like bats, falling and grooming. During aestivation, they compress the body and hang upside down from leaves, like bats hang from perches. They attach to the underside of leaves with mucus from a caudal gland. Disengagement is done with vigorous shell rotations and foot twisting in contorting sequences, and can be done as reaction to direct sunlight, and probably to avoid predators and parasites. They groom their own shell, shell lappets and foot, an unusual behavior among land snails. This species feeds mainly on epiphyllous mosses, algae and lichens, occasionally adding arthropod eggs and carrion. Egg laying is similar to other euconulids and valloniid snails. Conclusions: Aestivating hanging upside down is a drought avoiding trait described here for the first time and is also a new function for the caudal gland mucus. Leaf detaching is done by a contortion sequence of shell rotations and foot twisting; its complexity and duration varies according to the leaf side where the snail is located.

Attitude kinematics using slewing transformation of a single axis

Attitude kinematics using a single axis was developed to establish the relationships among the axis trajectory, enclosed solid angle and the associated attitude transformation. An arbitrary transformation due to a sequence of finite rotations or due to propagation consisting of an infinite number of infinitesimal rotations is equivalent to the product of a slewing transformation along a great circle arc linking the initial and final orientations of the axis followed by a rotational transformation about the axis. A key finding of this work is that the slewing transformation commutes with the rotational transformation, if the trajectory of the slewing transformation is fixed in space and the axis orientation is accounted for in the rotational transformation. The results were used to establish two new kinematic theorems. The new theorems provided simple derivations of Ishlinskii’s theorem, the Goodman-Roberson theorem and a result found by Montgomery. The findings in this work were applied to attitude propagation by separating attitude rotational increments that are normal to the axis with those that are parallel to the axis. The normal and parallel angular increments were integrated separately to form the slewing transformation and rotational transformation, respectively. The product of the two commuting transformations formed the total propagation transformation. The findings were validated by using them to create and implement a propagation algorithm. Numerical testing showed that the new algorithm has accuracy comparable to traditional attitude propagation algorithms when stress tested with pure coning motion.