singular gradient matrix at initial parameter estimates - Non Linear Regression

so I'm new to data science using R and I'm not sure what I'm doing wrong here. using the data set:

rocketBurn	Oxygen Consumed	Hydrogen Used	Trajectory	Thrust
20	20000	30000	0	500000
40	40000	60000	0	525000
60	60000	90000	0	551250
80	80000	120000	4	578813
100	100000	150000	8	593283
120	120000	180000	12	593283
140	140000	210000	16	593283
160	160000	240000	20	593283
180	180000	270000	24	593283
200	200000	300000	28	593283
220	220000	330000	32	593283
240	240000	360000	36	593283
260	260000	390000	40	593283
280	280000	420000	44	593283
300	300000	450000	46	593283
320	320000	480000	46	593283

I was able to create the linear regression model using the lm() formula in R, when I try to use the nls formula I am recieing the following error message

nlrModel <- nls(Trajectory ~ Oxygen.Consumed + Thrust,data = df,start = c(a=0,b=0,c=0))
Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff, nDcentral = nDcntr) : 
 singular gradient matrix at initial parameter estimates

After some googling I believe the error is due to the start parms, however, I don't know how to get the correct start parm. Any help on how to get this model to work would be greatly appreciated!

Solution

The problem is that the formula in the nls model is wrong. lm and nls do not use the same formula notation. In lm for a model with no interactions the independent variables are listed separated by plus signs whereas in nls the formula includes the coefficients. For example, this describes the same model in lm and nls.

lm(Trajectory ~ Oxygen.Consumed + Thrust, df)

st <- list(a = 1, b = 1, c = 1)
nls(Trajectory ~ a + b * Oxygen.Consumed + c * Thrust, df, start = st)

Note

The input in reproducible form is:

df <- 
structure(list(rocketBurn = c(20L, 40L, 60L, 80L, 100L, 120L, 
140L, 160L, 180L, 200L, 220L, 240L, 260L, 280L, 300L, 320L), 
    Oxygen.Consumed = c(20000L, 40000L, 60000L, 80000L, 100000L, 
    120000L, 140000L, 160000L, 180000L, 200000L, 220000L, 240000L, 
    260000L, 280000L, 300000L, 320000L), Hydrogen.Used = c(30000L, 
    60000L, 90000L, 120000L, 150000L, 180000L, 210000L, 240000L, 
    270000L, 300000L, 330000L, 360000L, 390000L, 420000L, 450000L, 
    480000L), Trajectory = c(0L, 0L, 0L, 4L, 8L, 12L, 16L, 20L, 
    24L, 28L, 32L, 36L, 40L, 44L, 46L, 46L), Thrust = c(500000L, 
    525000L, 551250L, 578813L, 593283L, 593283L, 593283L, 593283L, 
    593283L, 593283L, 593283L, 593283L, 593283L, 593283L, 593283L, 
    593283L)), class = "data.frame", row.names = c(NA, -16L))