Learning the High Bar Longswing:I. Task Dynamics and Emergence of the Coordination Pattern

Figures & data

Figure 1. Diagrammatic representation of the longswing with the gymnast rotating anti clockwise about the bar. The angular velocity about the circle angle Vicinanza et al. (2018) and angular position of the gymnasts during the functional phases of the shoulder and hip joints from Irwin and Kerwin (2005) are highlighted

Table 1. Testing and training schedule: Initial Assessment of subjects, ensuring physical ability and safety, followed by four Testing sessions interspersed by two training sessions over a four-week period

Initial Assessment	Week 1		Week 2		Week 3		Week 4
Physical ability and Safety	Testing session 1	Training sessions x2	Testing Session 2	Training sessions x2	Testing session 3	Training sessions x2	Testing session 4

Figure 2. Left: Schematic of CM and bar angular motion about the origin, defining the angle and angular velocity of the bar (θ_{b, ωb}) and CM (Θ_{CM, ωCM}). Continuous relative phase of the bar – CM interaction (right) within a trial. CRPθ_A (initiation of first out of phase sequence); CRPθ_B (initiation of second out of phase sequence) and CRPθ_C (end of second out of phase sequence)

Figure 3. Peak swing height, θcircle (°), for individual subjects (left) and Groups (right) for each testing day (1–4)

Figure 4. Vertical (_z) and horizontal (_y) CM and bar (Bar) position during the testing session 1–4, for two participants from Group 3 (top two rows) and two participants from the more successful Group 1 (bottom two rows). Group average angular position of the participants at the start and end of the hip (red arrow) and shoulder (blue arrow) functional phases for Group 3 (top two rows) and Group 1 (bottom two rows)

Figure 5. CM Dynamics during the Testing Session 1–4, for one participant from Group 1 (top row) and one participant from the least successful Group 3 (bottom row)

Table 2. Mean (m) and SD (s) of the angular position of the participant (Θc) at the start and end of the Functional phases of the hips (HΘc_start, HΘc_end) and shoulders (SΘc_start, SΘc_end) and joint angle (Θ) at the start and end of the Functional phases of the hips (HΘstart, HΘend) and shoulders (SΘstart, SΘend) during testing session 1–4

			Testing Session 1				Testing Session 2				Testing Session 3				Testing Session 4
			SΘstart	SΘend	HΘstart	HΘend	SΘstart	SΘend	HΘstart	HΘend	SΘstart	SΘend	HΘstart	HΘend	SΘstart	SΘend	HΘstart	HΘend
Θ	G1	m	4	56	−36	61	2	42	−26	58	5	41	−30	50	4	29	−26	48
		s	19	21	8	11	14	20	18	4	14	19	6	8	10	15	6	5
	G2	m	0	40	−30	50	12	50	−29	55	0	29	−26	52	1	31	−32	51
		s	13	25	13	20	18	24	8	8	13	13	10	13	10	17	6	9
	G3	m	−3	39	−36	56	−3	36	−33	60	−7	30	−35	63	0	37	−37	56
		s	17	11	9	18	16	14	4	8	16	13	10	9	16	13	6	15
			SΘc_start	SΘc_end	HΘc_start	HΘc_end	SΘc_start	SΘc_end	HΘc_start	HΘc_end	SΘc_start	SΘc_end	HΘc_start	HΘc_end	SΘc_start	SΘc_end	HΘc_start	HΘc_end
Θc	G1	m	163	238	116	209	176	249	121	216	182	260	90	214	173	231	105	217
		s	55	37	17	24	61	49	24	19	82	83	22	23	77	76	25	25
	G2	m	158	215	129	204	185	257	124	220	172	230	129	217	163	223	122	225
		s	46	50	34	25	44	22	17	19	50	51	18	16	46	57	31	20
	G3	m	160	210	123	193	171	233	127	205	159	210	131	209	181	244	113	197
		s	46	28	9	7	44	28	18	13	49	38	17	22	49	32	15	18

Figure 6. Group average for key continuous relative phase variables as a function of practice and skill level group

Figure 7. Individual participants continuous relative phase (CRP) of the CM – bar couple on testing day 1 and 4, against angular position of the gymnasts about the bar (θcircle). Highlighted are CRPθ_A (initiation of first out of phase sequence); CRPθ_B (initiation of second out of phase sequence) and CRPθ_C (end of second out of phase sequence). Top row represents group 3, middle row = group 2, bottom row = group 1

Table 3. Multiple step wise regression with maximum swing height (ΘMax_circle) as the dependent variables

Testing Day	Model	R	Adj R^2	Sig
1	CRPΘA, ω90°	0.57	0.53	P < 0.05
2	ω180°, CRPΘA, ω90°	0.87	0.85	P < 0.05
3	ω90°, CRPΘA	0.77	0.74	P < 0.05
4	CRPΘC, CRPΘA	0.93	0.92	P < 0.05

CRPθ_A = initiation of first out of phase sequence; CRPθ_C = end of second out of phase sequence; Angular velocity of the CM about the bar at 90° (ω90°) and 180° (ω180°) around the bar.

Table 4. Multiple step wise regression coefficients, constant and Beta (B). θMax_circle as the criterion variable and each model relates to a specific testing day

Testing day	DV	Model	Coefficient	B	Sig.	% contribution to R
1	ΘMaxcircle	Constant	296.7
		CRPΘA	−0.4	−0.5	P < 0.05	33.7
		ω90°	0.2	0.5	P < 0.05	23.2
2	Maxcircle	Constant	227.7
		ω180°	0.4	0.4	P < 0.05	72.4
		CRPΘA	−0.4	−0.3	P < 0.05	11.6
		ω90°	0.1	0.3	P < 0.05	2.9
3	ΘMaxcircle	Constant	304.5
		ω90°	0.2	0.5	P < 0.05	70.3
		CRPΘA	−0.9	−0.4	P < 0.05	6.3
4	ΘMaxcircle	Constant	138.9
		CRPΘC	0.6	−0.4	P < 0.05	90.1
		CRPΘA	−0.4	0.6	P < 0.05	2.4

CRPθ_A = initiation of first out of phase sequence; CRPθ_C = end of second out of phase sequence; Angular velocity of the CM about the bar at 90° (ω90°) and 180° (ω180°) around the bar. DV = dependent variable, B = beta. ΘMax_circle maximum swing height

Table 5. Linear regression matrix of the key variables associated with swing height

Testing day 1	ΘMaxcircle	PeakCRPΘB – CRPΘA	PeakCRPΘB – CRPΘC	CRPΘA	CRPΘB	CRPΘC	CRPΘB – CRPΘA	CRPΘC – CRPΘB	ω90°	ω180°
ΘMaxcircle	1	0.31	−0.24	−0.58*	−0.14	0.56*	0.17	0.35	0.58*	0.48*
PeakCRPΘB – CRPΘA	0.31	1	−0.34	−0.25	−0.16	0.47*	−0.04	0.34	0.34	−0.26
PeakCRPΘB – CRPΘC	−0.23	−0.34	1	0.11	−0.22	−0.28	−0.31	0.1	−0.21	−0.18
CRPΘA	−0.58*	−0.25	0.11	1	0.45*	−0.66*	−0.06	−0.68*	−0.18	−0.17
CRPΘB	−0.14	−0.17	−0.23	0.45	1	0.033	0.867	−0.918	0	−0.14
CRPΘC	0.56*	0.47*	−0.28	−0.66*	0.33	1	0.41*	0.36	0.13	−0.04
CRPΘB – CRPΘA	0.17	−0.04	−0.31	−0.06	0.87*	0.405	1	−0.647	0.13	−0.36
CRPΘC – CRPΘB	0.35	0.34	0.1	−0.68*	−0.92*	0.36	−0.64*	1	0.05	0.12
ω90°	0.58*	0.4	−0.21	−0.18	0	0.13	0.1	0.05	1	0.36
ω180°	0.47*	−0.26	−0.18	−0.17	−0.14	−0.04	−0.36	0.12	0.36	1
Testing day 4	ΘMaxcircle	PeakCRPΘB – CRPΘA	PeakCRPΘB – CRPΘC	CRPΘA	CRPΘB	CRPΘC	CRPΘB – CRPΘA	CRPΘC – CRPΘB	ω90°	ω180°
ΘMaxcircle	1	0.22	0.07	−0.93*	−0.17	0.95*	0.57*	0.71*	0.89*	0.84*
PeakCRPΘB – CRPΘA	0.23	1	−0.18	−0.13	−0.33	0.23	−0.16	0.38	0.03	0.1
PeakCRPΘB – CRPΘC	0.07	−0.18	1	−0.01	0.29	0.02	0.23	−0.19	−0.08	0
CRPΘA	−0.93*	−0.13	−0.01	1	0.13	−0.92*	−0.64*	−0.66*	−0.87*	−0.83*
CRPΘB	−0.17	−0.33	0.29	0.13	1	−0.12	0.67*	−0.79*	−0.17	−0.27
CRPΘC	0.95*	0.23	0.02	−0.92*	−0.12	1	0.59*	0.703	0.89	0.78*
CRPΘB – CRPΘA	0.57*	−0.16	0.23	−0.64*	0.67*	0.59	1	−0.12	0.51	0.41*
CRPΘC – CRPΘB	0.71*	0.38*	−0.19	−0.66*	−0.79*	0.7	−0.12	1	0.67*	0.68*
ω90°	0.89*	0.03	−0.08	−0.87*	−0.18	0.89*	0.51	0.67*	1	0.87*
ω180°	0.83*	0.11	0	−0.83*	−0.27	0.78*	0.41*	0.68*	0.87*	1

Vicinanza, D., Newell, K. M., Irwin, G., Smith, L., & Williams, G. K. R. (2018). Limit cycle dynamics of the gymnastics longswing. Human Movement Science, 57, 217–226. https://doi.org/10.1016/j.humov.2017.12.014

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