Simulation-based basketball training movement optimization and teaching guidance strategy

The ultimate loading to destruction at 1mm/min speed was carried out to calculate the mechanical indexes such as group modulus of elasticity, ultimate strength, yield strength, etc., and the modulus of elasticity of its pitching joints was calculated using equation (6). 6E=(F2−F1S)/(L2−L1L)×[Δσ−Δε]$$E = {{\left( {\frac{{{F_2} - {F_1}}}{S}} \right)} \bigg/ {\left( {\frac{{{L_2} - {L_1}}}{L}} \right)}} \times [\Delta \sigma - \Delta \varepsilon ]$$

where Δσ represents the stress difference, Δε represents the strain difference, S represents the stressed area of the trabecular sample during loading, and L represents the initial height of the trabecular sample before loading.

By taking the cutting modulus in loading in the 11th cycle as the initial modulus of elasticity of the sample, the initial modulus of elasticity at the time of pitching was calculated using equation (7): 7E0=σmax−σminεmax−εmin$${E_0} = \frac{{{\sigma_{\max }} - {\sigma_{\min }}}}{{{\varepsilon_{\max }} - {\varepsilon_{\min }}}}$$

where σ_max represents the cutting modulus, σ_min represents the average width of the medullary cavity between the trabeculae, ε_max represents the ratio of bone surface area to bone volume, and ε_min represents the range of stress variation in the dry femoral trabeculae [31].

Cyclic loading with a frequency of 2.0H_z was performed using the stress difference condition of E0Δσ=0.007$$\frac{{{E_0}}}{{\Delta \sigma }} = 0.007$$. Equation (8) was used to give the equation for the load during pitching: 8Fmax=0.007⋅E0⋅S+Fmin$${F_{\max }} = 0.007 \cdot {E_0} \cdot S + {F_{\min }}$$

where F_max and F_min represent the maximum and minimum values of the cyclic load.

Assuming that, from λ(l) represents the value of internal stress in the femoral neck of the human body and μ(e) represents the value of stress in the lateral side of the human body, the obtained F_max is used as a basis for calculating the characteristics of stress, strain changes in the model during impact loading using equation (9): 9BΣ(p)=μ(e)⊗∂(n)⇔η(Q)μ(Δ)×I(U)⊗λ(l)⊗l(w)∓Nm(a)Fmax$${B^{\Sigma (p)}} = \frac{{\mu (e) \otimes \partial (n) \Leftrightarrow \eta (Q)}}{{\mu (\Delta ) \times I(U) \otimes \lambda (l)}} \otimes \frac{{l(w) \mp {N^m}(a)}}{{{F_{\max }}}}$$

Where, ∂(n) represents the full node degree of freedom constraint of the inner and outer tree edges of the model, which is used as a boundary condition, η(Q) represents the stress distribution of the femur under the action of peak joint load, μ(Δ) represents the road tibial bundle perpendicular to the coronal plane of the human body, I(U) represents the change of the stress in the femur when the joint joint force passes through the center of the femoral head, ι(w) represents the point of action of the force of iliotibial bundle, and N^m(a) represents the point of action of the force of the adductor muscles.

Based on the results calculated in equation (9), equation (10) was utilized to obtain the stress values obtained in the horizontal direction when the joint force μ(d) transmitted by the femoral head was shifted at the point of action d for different angles: 10ε*(ι)=μ(d)×l(H)η(w)⊗Y(q)⇔B*(ν)$${\varepsilon^*}(\iota ) = \frac{{\mu (d) \times \ell (H)}}{{\eta (w)}} \otimes Y(q) \Leftrightarrow {B^*}(\nu )$$

Where, ℓ(H) represents the trend of femoral stress in outer tension and inner compression, Y(q) represents the change of femoral stress in cross-section, and B^k(ν) represents the effect of muscle on femoral gravity conduction.

Assuming, by ζ(j) represents the direction of femur force, analyze the mechanical indexes such as bone volume fraction of femur bone trabeculae, average thickness of bone trabeculae, and the number of elastic modulus cycles under different force directions, adjust the pitching postures based on these mechanical indexes, and complete the optimization training of the targeting technique of basketball players’ pitching by using Eq. (11). 11(BV/TV)=(BS/BV)(Tb/Th)⊕(Tb*SP)ζ(j)$$\left( {BV/TV} \right) = \frac{{(BS/BV)}}{{(Tb/Th)}} \oplus (Tb*SP)\zeta (j)$$

where BS represents the trabecular thickness, defining this value as a model-independent indicator of the 3D structure of the trabeculae, BV represents the average width of the medullary cavities between the trabeculae, Tb represents the bone volume fraction, Th represents an indicator of the spatial structure of the trabeculae, and SP represents the ratio of the bone surface area to the bone volume.

Fix the displacement of the basketball along the X-direction as 2450mm, change the displacement of the basketball along the Y-direction in turn, so that the angle between the combined displacement and the X-direction, i.e. the angle of the shot, is 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65° in turn. Thus, the basketball is thrown to the same distance and different heights to study the effect of different shooting heights on the trajectory of basketball movement. The effects of different shooting heights on the trajectory of the basketball are shown in Figure 1. From the figure, it can be observed that the shooting height is positively correlated with the shot angle, and the difference between the basketball trajectories increases gradually with the increase of the shooting height and the shot angle. The basketball becomes steeper in the descending section, i.e., the angle of incidence of the shot into the basket is larger, and it is easier to score. In addition, due to inertia, the basketball continues to move forward for a certain distance after the end of the first analyzed step, and this distance increases with the height of the shot, which is why the phenomenon of the X coordinate of the highest point in each curve gradually increases with the height of the shot.

Figure 1.

The impact of different shooting heights on the trajectory of basketball

The displacement of the basketball along the Y direction was fixed at 2056mm, and the displacement of the basketball along the X direction was changed, i.e., the basketball was thrown to the same height and different distances to study the effect of different shooting distances on the trajectory of the basketball. These shooting distances are also set according to different shot angles, with the increase of shooting distances, the corresponding shot angles in the X direction are 65°, 60°, 55°, 50°, 45°, 40°, 35°, 30°, 25°, 20°. The effects of different shooting distances on the trajectory of the basketball are shown in Figure 2. From the figure, it can be observed that the shooting distance and the shot angle are negatively correlated, with the decrease of the shooting distance and the increase of the shot angle, the flying distance of the basketball in the air decreases, which clearly shows the situation of “seeing high but not far”. In addition, with the increase of shooting distance and the decrease of shooting angle, the difference between the trajectories of the basketball gradually increases, and the basketball becomes flat in the descending section, which is unfavorable for it to be put into the basket.

Figure 2.

The effect of different shooting distances on the trajectory of basketball

In basketball, scoring is the ultimate goal. For this reason, when the shot angle is 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, the displacement of the basketball along the X direction and along the Y direction are adjusted at the same time, so as to obtain the trajectory of the basketball that can be shot and scored in different shot angles, and the trajectory of the basketball that can be scored in different shot angles is shown in Fig. 3. From the figure, it can be clearly observed that, with the gradual increase of the shot angle, in order to score a basket, it is necessary to gradually increase the height of the shot and reduce the distance of the shot, and vice versa. As the shot angle decreases, the angle of incidence of the basketball into the basket decreases, which is detrimental to the rim. This also illustrates the principle that it is difficult to score with a very flat shot. The literature states that the best angle of incidence is 38°-45°, and according to the results of the figure, the best angle of shot is measured to be 50°-55°, which coincides with the literature based on experiments to obtain the highest hitting rate at the free-throw line of the angle of shot is 52°-54°.

Figure 3.

The basketball trajectories that can score at different shooting angles

It can be found that the displacement of the basketball along the X-direction (i.e., shooting distance) and the displacement along the Y-direction (i.e., shooting height) are in an exponential function when the shot is scored, as shown in Equation (12): 12Y=35830e−11075+360$$Y = 35830{e^{ - \frac{1}{{1075}}}} + 360$$

According to the characteristics of core strength training and the requirements of basketball players in terms of physical fitness training, the corresponding core strength training program, i.e., the training program of group S, was developed. The core strength training program is divided into three stages, and its training program is designed as follows.

The first stage of core strength training is shown in Table 1. The training intensity is small to ensure that the tested basketball players are adapted to the core strength training. In the early stage of training, the main training requirement is to enable the athletes to be initially familiar with the core strength training method, and gradually begin to adapt to the corresponding training. Because some of the experimental subjects have not received systematic core strength training, so in the design and implementation of core strength training, we need to fully consider the actual situation, according to the actual needs and characteristics of the athletes to carry out the corresponding adjustment of the content of the training program, the first phase of the main purpose of the training is to let the athletes gradually master the main way of core strength training, and begin to adapt to this kind of training gradually. The first phase of training aims to enable athletes to gradually master the core strength training and begin to adapt to this training method.

The second phase of core strength training is shown in Table 2. The difficulty of the training will be increased to medium training intensity. Training tools such as elastic force bands, Swiss balls, and BOSUs are used in this phase to enhance the stability of the basketball players, while resistance training is added to the training with the aim of increasing the stimulation of the core muscles of the basketball players. Into the second stage, in order to be able to quickly play the effect of core strength training, you need to add some auxiliary training tools, and for some key actions to carry out the corresponding strengthening training. The core of the second stage of training is to strengthen the core muscle groups of basketball players, through this way of strengthening training to enhance the strength and stability of the core muscle groups of basketball players, and in the process of basketball players’ body balance, sports coordination, confrontation and other appropriate strengthening training, which is also an important way to improve the core strength of basketball players at this stage. This is also an important way to improve the core strength of basketball players at this stage.

The third phase of core strength training is shown in Table 3. Through the preliminary core strength training, the core muscle strength and collaborative strength of the trained basketball players were improved, and the difficulty of training in this phase was further increased. A variety of machinery is used to create an unstable state for the athlete’s body, with the aim of strengthening core strength and increasing the athlete’s stability and coordination during confrontation. In the third stage of core strength training, it is necessary to comprehensively improve the athletes’ physical fitness level and the corresponding core muscle group strength by means of core strength training, and the data are also tested and recorded according to the corresponding training content in the test.

The control group will be experimented according to the conventional traditional strength training methods, the main items of traditional strength training are familiar to basketball players in their daily training, so the main consideration in the development of traditional strength training program is the rigor of the control group, especially in the training time and intensity of training, the differences between the traditional strength training methods and the core strength training methods should be considered comprehensively, and basically to maintain the The differences between traditional strength training and core strength training should be taken into account, and basically maintain the consistency in training time and intensity. Traditional strength training was performed 3 times per week, with a total training time of 120 minutes, and after each set of movements was completed, a rest of about 5 minutes was taken in the middle. The training schedule for traditional strength training is shown in Table 4.

The knee joint angle contrast during different side cuts to touchdown is shown in Figure 7 (a~c represent knee flexion/extension, knee inversion/exversion, and knee internal/external rotation, respectively). The graph curves show the dynamic changes of the knee joint during the touchdown of different side-cut motions, with the gray background part (0-60%) representing the cushioning phase and the remaining part (60%-100%) the stirrup extension phase. There was no interaction between side-cut angle and touchdown pattern on peak knee angle (P>0.05). The effect of touchdown mode on peak knee angle was not statistically significant (P>0.05). In contrast, the effect of different lateral cut angles on peak flexion knee angle was significant (P<0.05). Specifically, a two-by-two comparison by the Bonferroni method showed that the peak flexion knee angle for 135° lateral cut angle > peak flexion knee angle for 90° lateral cut angle > peak flexion knee angle for 45° lateral cut angle. This suggests that the peak knee flexion angle increases accordingly as the lateral cut angle increases, regardless of the touchdown pattern. In particular, in the hindfoot touchdown pattern, the peak knee flexion angle was generally higher at each lateral cut angle than in the forefoot touchdown pattern. The difference in peak knee flexion angle between the anterior and posterior foot touch patterns was smaller when 45° lateral cuts were performed. In addition, when a 135° lateral cut was performed, the knee showed greater knee valgus and greater knee internal rotation in the forefoot touch pattern.

Figure 7.

The Angle of knee joint in different side cutting

The three-dimensional peak ground reaction force characteristics of the knee joint with different lateral cut angles and different touchdown patterns are shown in Table 5 (the effects of touchdown pattern, lateral cut angle and interaction on each biomechanical index, ①P<0.05, ②P<0.01. ③P<0.05 compared with 45° lateral cut angle, ④P<0.05 compared with 90° lateral cut angle. the effects of forefoot and hindfoot touchdown patterns on each index (⑤P<0.05, ⑥P<0.01). For the leftward ground reaction force, the main effects of touchdown pattern and lateral cut angle were statistically significant (P<0.05). The upward ground reaction force was 2.41±0.19 for the 45° lateral cut angle, 2.18±0.21 for the 90° lateral cut angle, and 1.8±0.26 for the 135° lateral cut angle by the A two-by-two comparison by Bonferroni’s method showed that the upward ground reaction force for 135° sidetrack angle < upward ground reaction force for 90° sidetrack angle < upward ground reaction force for 45° sidetrack angle.