Abstract Background: The squat is one of the most used exercises in the field of strength and conditioning. It is included as a core exercise in many sports training programmes to enhance athletic performance due to its biomechanical and neuromuscular similarities of a wide range of athletic movements. The barbell squat commonly used by athletes participating in resistance training and it is generally performed using regular athletic shoes or specially designed weightlifting shoes. However it is now getting more common to perform the barbell back squat in barefoot or in barefoot-inspired foot wear. Weightlifting shoes may be well known to weightlifters but to the noncompetitive lifters and professional athletes they are in general unfamiliar. It is believed that the structure of the weightlifting shoe supports proper squat mechanism. There is however limited scientific data reporting on the use of weightlifting shoes and therefore, it may be needed to investigate how weightlifting shoes affects the lower body lifting kinematics in the back squat compared to other conditions. Aim: The aim of the study was to compare the kinematic differences that appears in the sagittal plane when performing a barbell back squat wearing weightlifting shoes and barefoot. Method: Fifteen healthy participants (n=15) completed the study. The study included the barbell back squat in three sets of three repetitions on 50, 60 and 70% of the participant’s 1RM. The participants performed the movement in both weightlifting shoes and barefoot in an order randomly chosen and all movements was recorded with a digital camera from the sagittal plane. Results: The results showed that the angles were greater in the weightlifting shoe condition on all percentage. The results showed that there was no statistical significance in the hip angle at 50% of 1RM (p= 0,370) or at 70% (p = 0,053) but a statistical significance in the hip angle at 60 % (p = 0,028). The results showed no statistical significance in the ankle angle at 50% of 1RM (p = 0,997), 60% (p = 0,182) or 70 % (p = 0,332). Conclusion: Findings from this study did not demonstrate that there was a significant difference between performing a barbell back squat in weightlifting shoes and barefoot. More research is needed to investigate and compare more variables in the difference between performing a barbell back squat wearing weightlifting shoes and barefoot.

Despite the squat jump's intriguing dynamical properties and prevalence in athletics, there is a lack of information regarding the comprehensive functional role of muscles during the squat jump. To increase our understanding of the strategies the human body uses in accelerating joints and contributing energy to body segments, we incorporated experimental data from trained collegiate men and women into musculoskeletal computer simulations. We evaluated the simulations to determine fundamental coordination principles of the squat jump, and the effect of increased loading and gender on muscle strategies employed during the squat jump. Our results revealed that the plantar flexors and vasti were primarily involved in increasing the mechanical energy of the body, while the proximal muscles were primarily involved in redistributing energy throughout the body. The erector spinae muscles extended the lumbar spine, and contributed energy to the torso, while gluteus maximus and hamstrings extended the hip joint, and contributed energy to the pelvis. The vasti extended the knee joint, and contributed energy to the pelvis and torso. Our results suggested that the rectus femoris plays a critical role in converting rotational energy into vertical kinetic energy. Greater barbell loads reduced the rate of lumbar extension, and resulted in increased normalized energy contributions from soleus and vasti to the torso. When comparing the squat jumps between men and women, our results suggested that soleus and vasti are more active in men than women during the body-weight squat jump. / text

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

INTRODUCTION: Altered neuromuscular control and knee joint instability are commonly observed in populations with knee osteoarthritis (OA). Since knee OA is more prevalent in females, sex-related differences in muscle activation and movement strategies during activities of daily living (ADL) are theorized to be a contributing factor to the increased prevalence in females. PURPOSE: The aims of this thesis were: 1) identify sex differences in joint dynamics and muscle activation patterns in older adults with knee OA and healthy older adults; and 2) investigate whether differences in co-activation and dynamic knee joint stiffness exist between sexes in an OA and healthy populations. For both aims, squatting tasks were evaluated because it is a common and critical component in ADLs. METHODS: Thirty healthy individuals (15 females) and thirty individuals with knee OA (15 female) performed three two-legged squats at a self-selected pace on two force platforms. Hip, knee, and ankle sagittal and frontal plane joint angles, moments and powers were calculated and electromyography (EMG) of eight muscles crossing the knee joint was recorded for the test (OA affected or dominant) limb. Maximum voluntary isometric contractions were used to normalize the EMG data. Co-activation indices for six antagonist muscle pairings and dynamic knee joint stiffness (DKJS) were calculated for the acceleration and deceleration phases of squat descent and ascent. Two-way ANOVAs (Sex X OA status) were used to characterize differences in muscle activation patterns and movement strategies. RESULTS: For aim 1, decreased hip, knee and ankle sagittal plane range of motion was identified in the OA participants, with females showing the greater deficits compared to the males. Males with OA implemented a hip dominant strategy by increasing hip joint moments and decreasing knee joint moments compared to the females. Indifferent of joint status, females performed the squat with more hip adduction compared to males. Females with OA demonstrated greater hip adduction and knee valgus angles throughout the squat, contributing to the decrease in the frontal plane range of motion. Additionally, hip joint power was lower in all female participants compared to males while knee joint power was lower in the OA participants. For aim 2, females with OA, and to lesser extent males with OA had greater DKJS around peak knee flexion compared to the healthy participants. Co-activation indices revealed sex differences in neuromuscular control: Females with knee osteoarthritis had higher muscle activation magnitude and co-activation of antagonistic muscles, whereas the males used a more selective increase in hamstring co-activation and more balanced quadriceps-hamstring recruitment. CONCLUSION: Two-legged squats were able to detect sex and OA related functional deficits at the knee and adjacent hip and ankle joints. OA had a greater effect on the movement and neuromuscular control in females than males and the squat identified specific deficiencies that can be targeted for rehabilitation.

The purposes of this dissertation were to examine bilateral asymmetry as a factor of postactivation potentiation, examine and compare the acute effects of ballistic and non-ballistic concentric-only half-squats on squat jump performance, and compare the potentiation and temporal profiles of strong and weak subjects following potentiation protocols that included ballistic and non-ballistic concentric-only half-squats. The following are major findings of the dissertation. Squat jump performance may be acutely enhanced following ballistic concentriconly half-squats; however the changes in performance do not appear to be related to bilateral symmetry. Ballistic concentric-only half-squats acutely improve various squat jump performance variables at various time intervals; however the changes in performance are not related to the bilateral symmetry of the subject. Ballistic concentric-only half-squats produced superior acute potentiation effects with regard to jump height, peak power, and allometricallyscaled peak power as compared to non-ballistic concentric-only half-squats and a control protocol. Stronger subjects potentiated earlier and to a greater extent as compared to their weaker counterparts. This dissertation indicates that bilateral symmetry may not be considered as an underlying factor affecting postactivation potentiation. However, it is suggested that future research should continue to investigate the factors that are associated with postactivation potentiation. The findings of this dissertation also demonstrate the importance of how an individual performs a concentric-only squatting motion. By training with ballistic movements, a greater training stimulus may be achieved as compared to training with non-ballistic movements. While this dissertation discussed the acute potentiation differences between ballistic and nonballistic concentric-only half-squats, longitudinal research is needed to determine if different training effects result from each training method. This dissertation also supports that notion that stronger individuals may benefit more with regard to potentiation effects. In order to optimize performance and realize the greatest potentiation effects, it is recommended that greater levels of relative strength should be sought. It is suggested that further research is needed on the longitudinal differences in the potentiation effects an individual can realize based on their strength levels.

The purpose of this study was to determine the relationship between the Minimal Velocity Threshold (MVT) of 1RM and repetitions until failure testing conditions using the back squat exercise. Fourteen injury-free males with experience in the back squat volunteered to perform a 1RM and a submaximal (70% 1RM) repetitions until failure test, each during different testing sessions. Mean Concentric Velocity (MCV) was collected using a wireless inertia-measuring device. The last successful repetition in either condition was considered the MVT. A very small relationship between 1RM and repetitions until failure MVT was found (r=-0.135). There were no significant differences between testing sessions and the effect size was small (Cohen’s d=0.468) between each testing session. The small relationship and the non-significant p-value might suggest there is individual variance with MVT. In conclusion, the results of this study do not support a general MVT for the back squat comparing 1RM and submaximal repetitions until failure.