Learning the high bar longswing:II. energetics and the emergence of the coordination pattern

Figures & data

Figure 1. Group average of critical biomechanical energetic variables about the bar during testing sessions 1, 2, 3, and 4. Energetic variables include maximum energy input (E_max, J), rate of energy input (E_rate, Js⁻¹), angular position (θE_max, °), and angular velocity (ωE_max, °s⁻¹) when E_max occurs

Figure 2. Average percentage (%) contribution to total joint work from the knees (KW, green), hips (HW, red), and shoulders (SW, blue) during testing days 1–4, for groups: 1, 2, and 3

Figure 3. Joint work at the knees, hips and shoulders during testing sessions 1–4, for one participant from group 1 (top row) and one participant from the least successful group 3 (bottom row). Knees = green, Hips = Red, Shoulders = Blue

Table 1. Multiple stepwise regression with maximum swing height (θMax_circle) as the criterion variable (each model relates to a specific testing day)

Testing day	Model	R	Adj R^2	Sig
1	ω@90, EMax	0.687	0.423	p < 0.05
2	ω@180, ω@90	0.914	0.820	p < 0.05
3	ω@90, EMax	0.867	0.729	p < 0.05
4	ω@90, RateofEnergy	0.931	0.855	p < 0.05

E_Max = maximum energy; ω@90 = angular velocity at 90° circle angle; ω@180 = angular velocity at 180° circle angle; rate of energy = rate of energy input.

Table 2. Multiple stepwise regression coefficients, constant and Beta (B). θcircle as the criterion variable and each model relates to a specific testing day

Testing day	Criterion variable	Model	Coefficient	B	Sig.	% contribution
1	θMaxcircle	Constant	240.7
		ω@90	0.3	0.7	p < 0.05	33.6
		EMax	5.0	0.4	p < 0.05	13.5
2	θMaxcircle	Constant	171.8
		ω@180	0.2	0.5	p < 0.05	72.4
		ω@90	0.5	0.5	p < 0.05	11.2
3	θMaxcircle	Constant	251.4
		ω@90	0.3	0.8	p < 0.05	70.3
		EMax	6.6	0.2	p < 0.05	4.9
4	θMaxcircle	Constant	228.3
		ω@90	0.4	0.7	p < 0.05	78.5
		RateofEnergy	677.5	0.3	p < 0.05	8.1

E_Max = maximum energy; ω@90 = angular velocity at 90° circle angle; ω@180 = angular velocity at 180° circle angle; rate of energy = rate of energy input. θMax_circle maximum swing height

Table 3. Linear regression matrix of the key energy variables associated with swing height

Testing day 1	θMaxcircle	Energy^−1	θEMax	EMax	ω@90	ω@180	ω@EMax
θMaxcircle	1.00	−0.01	0.28	0.21	0.58*	0.48*	0.18
Energy^−1	−0.01	1.00	−0.35	0.23	−0.11	0.41*	0.22
θEMax	0.28	−0.34	1.00	0.66*	−0.01	−0.03	−0.68*
EMax	0.21	0.23	0.67*	1.00	−0.24	0.12	−0.42*
ω@90	0.58*	−0.10	−0.01	−0.24	1.00	0.34	0.32
ω@180	0.47*	0.41*	−0.03	0.12	0.34	1.00	0.40*
ω@EMax	0.17	0.21	−0.70*	−0.42*	0.32	0.40*	1.00
Testing day 4	θMaxcircle	Energy^−1	θEMax	EMax	ω@90	ω@180	ω@Emax
θMaxcircle	1.00	0.69*	0.74*	0.73*	0.87*	0.84*	−0.26
Energy^−1	0.69*	1.00	0.51*	0.66*	0.45*	0.52*	−0.20
θEMax	0.74*	0.51*	1.00	0.67*	0.68*	0.52*	−0.50*
EMax	0.73*	0.66*	0.66*	1.00	0.63*	0.59*	−0.32
ω@90	0.87*	0.50*	0.68*	0.63*	1.00	0.87*	−0.13
ω@180	0.84*	0.52*	0.52*	0.59*	0.87*	1.00	−0.04
ω@EMax	−0.23	−0.12	−0.50*	−0.32	−0.13	−0.04	1.00

θMax_circle = maximum swing angle, energy⁻¹ = rate of energy input, θE_Max = swing angle at E_Max, E_Max = maximum energy, ω@90 = angular velocity at 90° circle angle; ω@180 = angular velocity at 180° circle angle ω@E_Max = angular velocity at E_max. * = p < 0.05

Figure 4. Diagrammatic representation of the successful novice, continuous, longswing with the gymnast rotating anti-clockwise about the bar. The two-phase model blue semi-circle (exploiting free fall) and red semi-circle (energy Input) are interspersed a two transition 1. during the handstand phase and 2 during the energy input phase. The functional phase is highlighted and representative of energy input (E) for unsuccessful and successful novice longswing is illustrated by green arrows. The candidate collective variable: Continuous relative phase of the bar – centre of mass interaction is shown by the red dashed line. 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). CM dynamics (blue line: Radial angular velocity of CM) of a successful participant (P05) from the current study