esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Discussion  
Our study aimed to investigate potential differences in the WA results obtained from LD signals without and with correction for the COI. We investigated the effects of the COI on steady-state LD signal represented by the baseline LD signal and the complex transient signal acquired after the release of a temporal occlusion of the brachial artery. We hypothesized that the COI correction is necessary for the post-occlusion signal due to the initial high-perfusion transient, but that the COI correction might not be necessary for the baseline signal where edge effects are relatively small. To the best of our knowledge, this is the first study addressing the importance of COI in biological signals evaluating microcirculation.  
Our main finding is that adjusting the WA results for the COI correction is crucial in transient LD signals, but not necessary for baseline signals. The former is especially relevant for low-frequency intervals, the interpretation of which is questionable in practice. Failure to do so may lead to a misinterpretation of the results obtained and, consequently, to a misinterpretation of the effects of different physiological mechanisms on the microcirculatory response.  
The biological and physical background of LD signals is complex and requires a careful selection of the analytical tool. Given the complex interplay of different factors regulating microcirculatory responses in different settings, it is challenging to determine the separate contributions of each factor. Therefore, it is crucial to employ advanced techniques in the analysis to ensure accuracy and prevent misleading conclusions. Although studying microcirculatory dynamics using WA can provide useful and reliable insight into the properties of the signal [4; 19], potential inaccuracies in the results caused by edge effects have not yet been adequately addressed.
# Outdoor Node Localization Using Random Neural Networks for Large-Scale Urban IoT LoRa Networks +
## 4 Methodology
### Data Normalization  
The RSSI values of the used dataset are large and, due to large weights, the network becomes unstable. Therefore, we scaled the dataset using the Min-Max Normalization data preprocessing technique to the range of 0 to 1, with the formula that follows:  
\[x_{i}=\frac{RSSI_{i}-\text{min}(RSSI)}{\text{max}(RSSI)-\text{min}(RSSI)}, \tag{1}\]  
whereby the raw RSSI input data is \(RSSI=(RSSI_{1},\dots,RSSI_{n})\) and the resultant normalized data are \(x(i)\).  
Figure 3: The distribution of RSSI Values for Antwerp.  
Figure 2: A map showing a random sample of used data points [46].
# A Tool for Pre-Operational Daily Mapping of Floods and Permanent Water Using Sentinel-1 Data
## 4 Results
### Delivery of the Flood/Permanent Water Map to the End User  
After having processed all the tiles in which the S1 data acquired from one orbit are divided, the corresponding maps of flood/permanent water are resampled and reprojected to the reference spatial grid (Section 2.2). Then, they are mosaicked by merging them in one unique map, having pixel size of 20 \(\times\) 20 m\({}^{2}\), ready to be delivered to the end-user. By  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**CEMS Activation Code** & **Commission Error [\%]** & **Omission Error [\%]** \\ \hline EMSR359 & 0.6 & 19.9 \\ EMSR411 & 5.6 & 20.8 \\ EMSR417 & 12.7 & 18.7 \\ EMSR429 & 13.7 & 3.7 \\ EMSR437 & 11.7 & 16.2 \\ EMSR445 & 8.1 & 11.2 \\ EMSR492 & 21.4 & 30.5 \\ EMSR496 & 1.3 & 2.5 \\ EMSR501 & 1.6 & 32.0 \\ EMSR502 & 13.8 & 22.3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Commission and omission errors for the class of permanent water.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**CEMS Activation Code** & **Commission Error [\%]** & **Omission Error [\%]** \\ \hline EMSR359 & 14.2 & 14.7 \\ EMSR411 & 23.9 & 8.3 \\ EMSR417 & 10.6 & 13.7 \\ EMSR429 & 20.6 & 21.2 \\ EMSR437 & 23.3 & 17.4 \\ EMSR445 & 25.3 & 10.9 \\ EMSR492 & 14.3 & 13.8 \\ EMSR496 & 24.4 & 1.7 \\ EMSR501 & 10.1 & 15.1 \\ EMSR502 & 8.5 & 19.4 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Commission and omission errors for the class of open floodwater.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**CEMS Activation Code** & **Total Flooded Surface** & **Total Flooded Surface** & **Total Flooded Surface** \\
**Code** & **Estimated by CEMS** & **Estimated by CEMS** & **Estimated by** **AUTOWADE [\%]** \\ \hline EMSR359 & 283 & 244 & 1.0 & 0.9 \\ EMSR411 & 285 & 330 & 0.7 & 0.8 \\ EMSR417 & 9460 & 8602 & 6.4 & 5.8 \\ EMSR429 & 546 & 553 & 6.9 & 7.0 \\ EMSR437 & 1850 & 1408 & 4.5 & 3.5 \\ EMSR445 & 1358 & 1607  
performing the operations of resampling, reprojection, and mosaicking, the daily map of floodwater/permanent water on a national (Italian) scale is created and made available on a web-portal of the Italian DCP developed by CIMA Research Foundation named MyDewetra [50].  
To make available the maps on MyDewetra, they are transformed in a vector file whose size in MB is considerably smaller than that of the original raster. This file is automatically delivered to MyDewetra to be visualized.  
An example of how a daily map is presented to the end-user through MyDewetra is shown in Figure 14. Panel (a) shows what appears to the end-user when he/she opens MyDewetra and chooses a day of interest (9 December 2020, in this case, when a flood event affected Northern Italy). Panels (b) and (c) are two zooms on the areas mostly affected by the flood.
## 3 Materials and Methods
### Proposed Method  
#### 3.3.1 Sliding-Window Computation Network  
The overall framework of the proposed method is illustrated in the figure and comprises an encoder and a decoder. As shown in Figure 1, the effective processing and integration of multimodal data are achieved through the design of a sliding-window attention mechanism and cross-layer blocks. The input consists of preprocessed multimodal data (e.g., images and time-series data), which, after passing through the feature extraction module, is fed into the encoder to generate multi-scale feature representations. These features are progressively reconstructed in the decoder to produce high-resolution predictions. The preprocessed input data are divided into multi-scale feature maps denoted as \(F_{1},F_{2},F_{3},F_{4}\), where \(F_{1}\) represents the highest-resolution feature map and \(F_{4}\) represents the lowest resolution. In the encoder, each feature map is processed through the sliding-window attention mechanism, resulting in multi-head attention representations \(M_{i}\). The sliding-window attention mechanism divides the feature maps into local windows, where self-attention is computed for features within each window. The resulting multi-scale feature maps \(M_{1},M_{2},M_{3},M_{4}\) are then passed to the cross-layer block, which facilitates feature complementation across layers. Cross-layer blocks employ residual connections to fuse information from the encoder and decoder, enhancing feature expressiveness. In the decoder, the outputs of the cross-layer blocks, denoted as \(D_{1},D_{2},D_{3},D_{4}\), are processed through upsampling modules to restore feature resolution, resulting in high-resolution feature maps \(D_{1}^{up},D_{2}^{up},D_{3}^{up},D_{4}^{up}\). These feature maps are concatenated along the channel dimension and further transformed using a multi-layer perceptron (MLP), producing the final high-resolution output mask. Throughout this process, the encoder leverages the synergy between the sliding-window attention mechanism and cross-layer blocks to extract multi-scale features and facilitate cross-layer interaction. Meanwhile, the decoder integrates these multi-scale features through progressive upsampling and fusion operations, culminating in high-resolution predictions. This design efficiently utilizes both global and local information in multimodal data, significantly improving model performance and computational efficiency.
# Structural Methodologies for Distributed Fault Detection and Isolation
## 4 Equation-Based Distributed Fault Detection and Isolation
### Maximum Detectability
```
1:input:\(S_{i}=\{V_{i}\), \(M_{i}\), \(E_{i}\), \(F_{i}\}\)
2:Let \(V_{\mathit{ishared}}\) be the set of shared variables in \(S_{i}\)
3:\(DF=\text{Detectable-Faults}(V_{\mathit{ishared}}\), \(S_{i})\)
4:Let \(V_{\mathit{im}}\) be \(V_{\mathit{ishared}}\)
5:for each\(v_{is}\in V_{\mathit{im}}\)do
6: Let \(V_{\mathit{im}}\) be \(V_{\mathit{im}}/v_{is}\)
7:if Detectable-Faults(\(V_{\mathit{im}}\), \(S_{i}\)) not equal \(DF\)then
8:\(V_{\mathit{im}}=V_{\mathit{im}}\cup\{v_{is}\}\)
9:return\(V_{\mathit{im}}\)
```  
**Algorithm 3** Minimal shared variables. Note that all of the shared unknown variables may not be measured. However, in some cases, it is possible to transfer a set of equations from the neighboring subsystems that can be used with the equations in the subsystem to compute the unknown variables.
# A Low-Power WLAN Communication Scheme for IoT WLAN Devices Using Wake-Up Receivers
## 6 Simulation Results and Discussion
### Simulation Results  
The measured delay of the transmission is depicted in Figure 13a. In the single-user transmission, the total delay to obtain the data from all STAs increased linearly as the number of STA increased. The rapid increase in the delay as the number of STAs increased is because of the repetition of the wake-up delay which the AP waited for the STA to wake up without processing other transmissions with regards to the procedure for obtaining the sensed data. There was little difference in the total transmission delays for the conventional method and unicast-MAC method. This is because the delay was mainly caused by the wake-up delay and the triggering frame transmission failure where the AP needed to retransmit the wake-up packet. Therefore, the effect of the contention delay for data packets appears to be limited.  
The MU transmission significantly reduced the transmission delay because the wake-up delay was reduced as the transmission procedure was done with multiple STA simultaneously. In addition to the MU operation as in IEEE 802.11 ax, the implementation of the scheduling scheme further reduced the transmission delay as it utilized the wake-up delay in the transmission procedure of the data packet and the wake-up packet addressed to other STAs. The difference between the multicast-MAC  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Name of Parameter** & **Value** \\ \hline \(T_{WULdelay}\) & wake-up delay & 10 ms \\ \(B\) & number of data bits & 1000 bit \\ \(P_{TX\_single}\) & Tx power for single user transmission & 280 mW \\ \(P_{TX\_mu}\) & Tx power for multiuser transmission & 280 mW \\ \(P_{RX}\) & receive power & 100 mW \\ \(P_{listen}\) & power for idle listening & 50 mW \\ \(P_{ST}\) & setup power & 5 mW \\ \(T_{D}\) & mean inter-arrival time of packet & 100 ms \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation Parameters. Tx = Transmit.  
scheme and the multicast-scheduled scheme increased as the number of STA increased. In the case of 100 STAs, the delay of the multicast-scheduled scheme was more than 40% smaller than the delay of the multicast-MAC scheme. The modification of the EDCA parameter in the TF also reduced the delay. This is because collisions of TFs resulted in a long wake-up delay because of the need to retransmit the wake-up frame to the corresponding STAs.  
From the perspective of the power consumption in each STA, the measured power was independent of the number of STAs, as shown in Figure 13b. The average power consumption in the MU transmission was higher because the length of the uplink data frame was increased significantly, as multiple STAs transmitted the frame simultaneously in the same bandwidth. In addition, the collision probability of the TF increased for MU transmission, which degraded the power efficiency. By adopting the modification of the EDCA parameter, the consumed power can be reduced in the MU transmission procedure.
## 3 Construction of a Risk Evaluation Model for Hazardous Chemical Road Transportation Accidents
### Determination of the Accident Risk Evaluation Methodology
#### 3.1.2 Determination of Objective Weights Based on the Entropy Weight Method  
The entropy weight method determines objective weights based on the magnitude of the variability of indicators. It can reflect, in depth, the differentiation ability of indicators, determine the best weights, and make the assignment more objective. Additionally, calculation is easy. In this paper, the entropy weight method is applied to determine the objective weights of risk factors for hazardous chemical road transport accidents, and the calculation steps are as follows [21; 22].  
(1) Construct the numerical matrix. Let the model have n secondary evaluation indicators and m primary evaluation indicators. \(x_{ij}(i=1,2,3,\ldots,m;j=1,2,3,\ldots,n)\) is the value of the jth evaluation indicator under the ith primary evaluation indicator, forming a numerical matrix \(X_{ij}\) of evaluation indicators of order \(m\times n\).  
\[X_{ij}=\left(\begin{array}{ccc}X_{11}&\ldots&X_{1n}\\ \vdots&\ddots&\vdots\vdots\\ X_{m1}&\ldots&X_{mm}\end{array}\right) \tag{4}\]  
(2) Standardize the indicators. Equation (5) is used to standardize positive indicators, and Equation (6) is used to standardize negative indicators.  
\[L_{ij}=\frac{X_{ij}-X_{\text{min}}}{X_{\text{max}}-X_{\text{min}}} \tag{5}\]  
\[L_{ij}=\frac{X_{\text{max}}-X_{ij}}{X_{\text{max}}-X_{\text{min}}} \tag{6}\]  
where (5) is the normalization of positive indicators, and (6) is the normalization of negative indicators, \(X_{\text{min}}\), \(X_{\text{max}}\) are the minimum and maximum values of the same criterion element index, respectively, and \(L_{ij}\) is the standardized \(X_{ij}\).  
(3) Calculate the weight value of the evaluation indicators. Calculate the weight value \(T_{ij}\) of the jth secondary evaluation indicator of the evaluation unit relative to the ith primary evaluation indicator.  
\[T_{ij}=\frac{L_{ij}}{\sum_{l=1}^{m}L_{ij}} \tag{7}\]  
(4) Calculate the entropy value of the index. Calculate the entropy \(E_{j}\) of the output of the jth evaluation index.  
\[E_{j}=-\frac{1}{\ln m}\sum_{i=1}^{m}T_{ij}\ln T_{ij} \tag{8}\]  
(5) Calculate the objective weights of the indicators.  
\[W_{j}=\frac{1-E_{j}}{\sum_{i=1}^{n}1-E_{j}} \tag{9}\]
# The Application of Augmented Reality in the Automotive Industry: A Systematic Literature Review
## Results
### Application Areas
#### 3.4.1 AR in Designing, Manufacturing, Training, Maintenance and Customer Support  
Automobile companies have introduced AR technology in manufacturing environments for assembly, maintenance or inspection tasks. Typical tasks can benefit from AR by providing assistance to operators using different types of information superimposed in the work environment, supplemented with other technologies like telepresence systems [33]. In addition, technicians can use AR-based systems which provide on-site instructions (in front of their eyes) about the methodology they need to adopt [14] for vehicle diagnostics and repair, such as how and where to act, thus reducing the learning time and mental effort [24]. Therefore, even inexperienced people can be turned into mechanics by following the instructions provided through AR applications for the maintenance of their own cars [34], following 2D or 3D instructions on a mobile device [35].  
The advantages of AR have been explored by car manufacturers through major collaborative projects, from car design to customer support services [18]. AR provides operators with the necessary  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **Year of Publication** & **Time Span** & **Databases** & **No. of Articles** &
\begin{tabular}{c} **Articles in** \\ **Automotive [\%]** \\ \end{tabular} \\ \hline
[30] & 2016 & 2010–2016 & Scopus & 466 & 100\% \\ \hline
[21] & 2019 & 2006–2017 &
\begin{tabular}{c} Scopus, Web of \\ Science, Ebsco \\ \end{tabular} & 174 & 6\% \\ \hline
[32] & 2016 & N/A & N/A & N/A & 100\% \\ \hline
[1] & 2015 & 2001–2015 & N/A & 39 & 24\% \\ \hline
[22] & 2014 & 1992–2014 & N/A & 57 & 100\% \\ \hline
[4] & 2018 & N/A &
\begin{tabular}{c} Google \\ Scholar, Ebsco \\ \end{tabular} & N/A & 100\% \\ \hline
[31] & 2017 & 1987–2016 & N/A & N/A & 100\% \\ \hline
[25] & 1999 & 1993–1998 & N/A & N/A & N/A \\ \hline
[7] & 2019 & 1994–2019 & N/A & 112 & N/A \\ \hline
[27] & 2014 &
\begin{tabular}{c} Scopus, \\ Science Direct, \\ Google Scholar \\ \end{tabular} & 147 & N/A \\ \hline
[26] & 2012 & 1990–2011 & N/A & 187 & N/A \\ \hline
[23] & 2019 & 1994–2016 &
\begin{tabular}{c} ACM digital \\ library, Science \\ Direct, Scopus, \\ Web of Science \\ \end{tabular} & 44 & 100\% \\ \hline
[24] & 2005 & 2001–2004 & N/A & 10 & N/A \\ \hline
[28] & 2017 & 2005–2016 &
\begin{tabular}{c} Scopus, \\ Google Scholar \\ \end{tabular} & 165 & N/A \\ \hline
[29] & 2019 & 2014–2019 &
\begin{tabular}{c} IEEE Xplore, \\ Science Direct, \\ Scopus, Google \\ Scholar, Web \\ Engineering Village \\ \end{tabular} & 49 & 41\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of review papers.  
documentation information at the right time, reducing the mental effort they have to make: 2D or 3D information can be provided, animated or not, related to the execution procedure, steps to be taken, the tool used or the task to be performed.
# PTMD Control on a Benchmark TV Tower under Earthquake and Wind Load Excitations
## 4 Improved Bounding Model
### Parameter Tuning  
For the selected material, the parameters for both the traditional Hertz-based model, as well as the five parameters for the modified bounding model, are optimized. The minimization problem is defined and the following residual vector is to be minimized:  
\[J=\mathbf{R}^{T}\mathbf{W}\mathbf{R} \tag{16}\]  
\[\mathbf{R}=\left\{\begin{array}{cc}\mathbf{R}^{p}&\mathbf{R}^{s}\\ \end{array}\right\}^{T} \tag{17}\]  
Figure 3: Pounding force and displacement recorded during the experiment.  
Figure 2: Experimental setup for the validation experiment. Upon excitation of the motor, the horizontal rod holding the mass will impact repeatedly on the viscoelastic layer.  
Here \(\mathbf{W}\) is a weighting factor applied to different residual items, \(\mathbf{R}^{p}\) represents the differences of the peak bounding force between the experimental and simulation data, and \(\mathbf{R}^{s}\) represents the similarity of the bounding force vector. \(\mathbf{R}^{p}\) and \(\mathbf{R}^{s}\) are defined as:  
\[\mathbf{R}^{p}(i)=\frac{\left|\max(F^{\text{E}})-\max(F^{\text{S}})\right|}{\max(F ^{\text{E}})} \tag{18}\]  
\[\mathbf{R}^{\text{S}}(i)=1-\frac{\left\{\phi_{i}^{\text{E}}\right\}^{T}\!\!\left\{ \phi_{i}^{\text{S}}\right\}}{\left(\left\{\phi_{i}^{\text{E}}\right\}^{T}\! \!\left\{\phi_{i}^{\text{E}}\right\}\right)\!\left(\left\{\phi_{i}^{\text{S}} \right\}^{T}\!\!\left\{\phi_{i}^{\text{S}}\right\}\right)} \tag{19}\]  
in which \(\left\{\phi\right\}\) is the bounding force vector, the superscripts 'E' and 'S' represent the items associated with the experimental and the simulated data, respectively, and 'T' denotes vector (matrix) transpose.  
A Hertz contact law-based bounding model is adopted in the previous study by [PERSON] et al. [34]. In the previous model, only the bounding stiffness \(\beta\) needs to be estimated. In this modified model, a trust-region based optimization method with global minimization is adopted to decide the parameters \(\beta_{1},\xi_{2},s_{1},s_{2}\). Ten sets of bounding data were chosen for model tuning and the optimized parameters are listed in Table 1. The tuned model is then used to predict the bounding force from the recorded displacement. The comparison of the simulated and experimental bounding force is shown in Figure 4. An obvious improvement is observed from these figures. By compensating the influence of the changing impact damping, the proposed model can now better predict the peak value of the bounding force during impact.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & \(\mathbf{\beta_{1}}\) & \(\mathbf{\xi_{2}}\) & \(\mathbf{s_{1}}\) & \(\mathbf{s_{2}}\) \\ \hline value & 10,560 & 0.8 & 1.3 & 1.1 \\ \hline \end{tabular}
\end{table}
Table 1: Optimized parameters of the modified bounding model.  
Figure 4: _Cont._
# Design and Analysis of a Planar Six-Bar Crank-Driven Leg Mechanism for Walking Robots
## 4 Kinematic Analysis
### Acceleration Analysis  
To obtain an expression for the angular accelerations of links 3 and 4, we differentiate Equation (17) with respect to time. The equation then becomes  
\[\left(-a\omega_{2}^{2}e^{i\theta_{2}}\right)+\left(ba_{3}je^{i\theta_{3}}-b \omega_{3}^{2}e^{i\theta_{3}}\right)-\left(ba_{4}je^{i\theta_{4}}-b\omega_{4} ^{2}e^{i\theta_{4}}\right)=0 \tag{24}\]  
This equation leads to two scalar equations which can be solved simultaneously for \(\alpha_{3}\) and \(\alpha_{4}\).  
\[\alpha_{3}=\frac{PQ-NS}{NR-OQ} \tag{25}\]  
\[\alpha_{4}=\frac{PR-OS}{NR-OQ} \tag{26}\]  
where  
\[N=c\mathrm{sin}\,\theta_{4} \tag{27}\]  
\[O=b\mathrm{sin}\,\theta_{3} \tag{28}\]  
\[P=a\alpha_{2}\,\mathrm{sin}\theta_{2}+a\omega_{2}^{2}\mathrm{cos}\,\theta_{2 }+b\omega_{3}^{2}\mathrm{cos}\,\theta_{3}-b\omega_{4}^{2}\mathrm{cos}\,\theta _{4} \tag{29}\]  
\[Q=c\mathrm{cos}\,\theta_{4} \tag{30}\]  
\[R=b\mathrm{cos}\,\theta_{3} \tag{31}\]  
\[S=a\alpha_{2}\mathrm{cos}\,\theta_{2}-a\omega_{2}^{2}\mathrm{sin}\,\theta_{2 }-b\omega_{3}^{2}\mathrm{sin}\,\theta_{3}-b\omega_{4}^{2}\mathrm{sin}\,\theta _{4} \tag{32}\]  
Furthermore, the angular accelerations of the links are influenced by the pantograph's geometry. The angular accelerations \(\alpha_{4}\) and \(\alpha_{6}\) are equal because the acceleration of one link directly affects the acceleration of the other link within the pantograph. This mechanical linkage ensures that any change in rotational speed is mirrored in the corresponding link. Similarly, the angular accelerations \(\alpha_{5}\) and \(\alpha_{3}\) are equal because the pantograph mechanism distributes the angular acceleration equally among the corresponding links. This ensures that the movement of the leg mechanism remains precise and predictable, which is essential for its proper functioning.  
\[\alpha_{5}=\alpha_{3} \tag{33}\]  
\[\alpha_{6}=\alpha_{4} \tag{34}\]  
The acceleration components of the foot contact point P are calculated by the numerical differentiation of velocity Equations (22) and (23):  
\[\begin{split} a_{P_{x}}=-a\omega_{2}^{2}\mathrm{cos}\,\theta_{2 }-a\alpha_{2}\mathrm{sin}\,\theta_{2}-l\omega_{3}^{  
+++ ==WARNING: Truncated because of repetitions==
2}\mathrm{cos}(\theta_{3}- \gamma)-la_{3}\mathrm{sin}\,(\theta_{3}-\gamma)+c\omega_{4}^{2}\mathrm{cos}\, \theta_{4}+c\alpha_{4}\mathrm{sin}\,\theta_{4}-f\omega_{4}^{2}\mathrm{cos}( \theta_{4}+\beta)\\ -f\alpha_{4}\mathrm{sin}(\theta_{4}+\beta)\end{split}\] (35)  
\[\begin{split} a_{P_{y}}=-a\omega_{2}^{2}\mathrm{sin}\,\theta_{2 }+a\alpha_{2}\mathrm{cos}\,\theta_{2}-l\omega_{3}^{2}\mathrm{sin}(\theta_{3}- \gamma)+la_{3}\mathrm{cos}\,(\theta_{3}-\gamma)+c\omega_{4}^{2}\mathrm{sin}\, \theta_{4}-c\alpha_{4}\mathrm{cos}\,\theta_{4}-f\omega_{4}^{2}\mathrm{sin}( \theta_{4}+\beta)\\ -f\alpha_{4}\mathrm{cos}(\theta_{4}+\beta)\end{split}\] (36)